Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
454 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #22598789 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22590022 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #22590004 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #22586498 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #22586497 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22586496 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | C71×#1406 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14556155 | — | 2 | 1 | no | — |
| 9 | C2×#14556152 | — | 2 | 1 | no | — |
| 10 | #17986548 | C22 | 1 | 1 | yes | characteristic |
| 11 | #127×D71 | C4 | 1 | 1 | yes | characteristic, complemented |
| 12 | #17986389 | C22 | 1 | 1 | yes | characteristic |
| 13 | #17986388 | C4 | 1 | 1 | yes | characteristic, complemented |
| 14 | #17986386 | C4 | 1 | 1 | yes | characteristic, complemented |
| 15 | #17986374 | — | 2 | 1 | no | — |
| 16 | #17986370 | — | 2 | 1 | no | — |
| 17 | #17985982 | — | 2 | 1 | no | — |
| 18 | #17985971 | — | 2 | 1 | no | — |
| 19 | #17985951 | C4 | 1 | 1 | yes | characteristic, complemented |
| 20 | #17985797 | — | 2 | 1 | no | — |
| 21 | #17985796 | C22 | 1 | 1 | yes | characteristic, complemented |
| 22 | #17985794 | C22 | 1 | 1 | yes | characteristic, complemented |
| 23 | #17985791 | — | 2 | 1 | no | — |
| 24 | #496×C71 | C22 | 1 | 1 | yes | characteristic |
| 25 | #355×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 26 | #354×C71 | C22 | 1 | 1 | yes | characteristic, complemented |
| 27 | C2×#11765866 | D4 | 1 | 1 | yes | characteristic |
| 28 | C2×#11765864 | D4 | 1 | 1 | yes | characteristic |
| 29 | C2×D4×D71 | — | 2 | 1 | no | — |
| 30 | C2×D4×D71 | — | 4 | 1 | no | — |
| 31 | #14556155 | — | 4 | 2 | no | — |
| 32 | #14556155 | — | 4 | 2 | no | — |
| 33 | #14556152 | — | 4 | 2 | no | — |
| 34 | #14556152 | — | 4 | 2 | no | — |
| 35 | C2×#11765854 | — | 2 | 1 | no | — |
| 36 | C2×#11765853 | — | 2 | 1 | no | — |
| 37 | C2×#11765852 | — | 2 | 1 | no | — |
| 38 | C2×D568 | — | 2 | 1 | no | — |
| 39 | C2×#11765850 | — | 2 | 1 | no | — |
| 40 | C2×#11765850 | — | 2 | 1 | no | — |
| 41 | C2×#11765848 | — | 2 | 1 | no | — |
| 42 | M16×D71 | — | 4 | 1 | no | — |
| 43 | #14556126 | D4 | 1 | 1 | yes | characteristic |
| 44 | #14556125 | C2×C4 | 1 | 1 | yes | characteristic |
| 45 | #14556124 | — | 2 | 1 | no | — |
| 46 | #14556124 | — | 4 | 1 | no | — |
| 47 | #14556124 | D4 | 1 | 1 | yes | characteristic |
| 48 | #14556116 | C2×C4 | 1 | 1 | yes | characteristic |
| 49 | #14556101 | — | 4 | 1 | no | — |
| 50 | (C22⋊D71)⋊C4 | — | 4 | 1 | no | — |
| 51 | #14556084 | — | 4 | 1 | no | — |
| 52 | C42×D71 | C2×C4 | 1 | 1 | yes | characteristic |
| 53 | #14556047 | — | 2 | 1 | no | — |
| 54 | #14556044 | — | 4 | 1 | no | — |
| 55 | #14556043 | — | 2 | 1 | no | — |
| 56 | #14556042 | — | 4 | 1 | no | — |
| 57 | #14556039 | C2×C4 | 1 | 1 | yes | characteristic |
| 58 | C8×Dic71 | — | 2 | 1 | no | — |
| 59 | C2×SD16×C71 | — | 2 | 1 | no | — |
| 60 | C2×D8×C71 | — | 2 | 1 | no | — |
| 61 | #127×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 62 | #124×C71 | C23 | 1 | 1 | yes | characteristic |
| 63 | #101×C71 | — | 2 | 1 | no | — |
| 64 | #99×C71 | — | 2 | 1 | no | — |
| 65 | #97×C71 | C2×C4 | 1 | 1 | yes | characteristic |
| 66 | C23×D71 | — | 4 | 1 | no | — |
| 67 | #11765866 | — | 4 | 1 | no | — |
| 68 | #11765866 | — | 4 | 1 | no | — |
| 69 | #11765864 | — | 4 | 1 | no | — |
| 70 | #11765864 | — | 4 | 1 | no | — |
| 71 | C2×Dic142 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 72 | C2×D284 | — | 2 | 1 | no | — |
| 73 | C2×D284 | — | 2 | 1 | no | — |
| 74 | C2×D284 | — | 4 | 1 | no | — |
| 75 | C2×D284 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 76 | C2×C22⋊D71 | — | 2 | 1 | no | — |
| 77 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 78 | C2×C22⋊D71 | — | 4 | 2 | no | — |
| 79 | C2×C22⋊D71 | — | 4 | 1 | no | — |
| 80 | D4×D71 | — | 4 | 1 | no | — |
| 81 | D4×D71 | — | 4 | 1 | no | — |
| 82 | D4×D71 | — | 4 | 1 | no | — |
| 83 | D4×D71 | — | 4 | 1 | no | — |
| 84 | D4×D71 | — | 8 | 4 | no | — |
| 85 | C22×Dic71 | — | 2 | 1 | no | — |
| 86 | C2×C4×D71 | — | 2 | 1 | no | — |
| 87 | C2×C4×D71 | — | 2 | 1 | no | — |
| 88 | C2×C4×D71 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 89 | #11765854 | — | 4 | 2 | no | — |
| 90 | #11765853 | — | 4 | 2 | no | — |
| 91 | #11765852 | — | 4 | 2 | no | — |
| 92 | D568 | — | 4 | 2 | no | — |
| 93 | #11765850 | — | 4 | 2 | no | — |
| 94 | #11765850 | — | 4 | 2 | no | — |
| 95 | #11765849 | — | 4 | 1 | no | — |
| 96 | #11765848 | — | 2 | 2 | no | — |
| 97 | #11765848 | — | 2 | 2 | no | — |
| 98 | #11765848 | — | 8 | 1 | no | — |
| 99 | C2×C71⋊C8 | — | 2 | 1 | no | — |
| 100 | C8×D71 | — | 8 | 1 | no | — |
| 101 | Dic71⋊C4 | — | 4 | 1 | no | — |
| 102 | Dic71⋊C4 | — | 8 | 1 | no | — |
| 103 | C22⋊Dic71 | — | 4 | 1 | no | — |
| 104 | (C2×D71)⋊C4 | — | 4 | 1 | no | — |
| 105 | C4×Dic71 | — | 2 | 1 | no | — |
| 106 | C4×Dic71 | — | 8 | 1 | no | — |
| 107 | C4×Dic71 | C22⋊C4 | 1 | 1 | yes | characteristic |
| 108 | C2×Q8×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 109 | C2×D4×C71 | — | 2 | 1 | no | — |
| 110 | C2×D4×C71 | — | 4 | 1 | no | — |
| 111 | C2×D4×C71 | C2×D4 | 1 | 1 | yes | characteristic |
| 112 | SD16×C71 | — | 4 | 2 | no | — |
| 113 | D8×C71 | — | 4 | 2 | no | — |
| 114 | M16×C71 | — | 4 | 1 | no | — |
| 115 | C2×C8×C71 | — | 2 | 1 | no | — |
| 116 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 117 | C22⋊C4×C71 | — | 4 | 1 | no | — |
| 118 | C42×C71 | C22×C4 | 1 | 1 | yes | characteristic |
| 119 | C23×C71 | — | 2 | 1 | no | — |
| 120 | C23×C71 | — | 4 | 1 | no | — |
| 121 | C22×D71 | — | 2 | 1 | no | — |
| 122 | C22×D71 | — | 4 | 1 | no | — |
| 123 | C22×D71 | — | 8 | 1 | no | — |
| 124 | C22×D71 | — | 8 | 1 | no | — |
| 125 | C22×D71 | — | 8 | 4 | no | — |
| 126 | C22×D71 | #99 | 1 | 1 | yes | characteristic |
| 127 | Q8×C71 | — | 4 | 1 | no | — |
| 128 | D4×C71 | — | 4 | 1 | no | — |
| 129 | D4×C71 | — | 4 | 1 | no | — |
| 130 | D4×C71 | — | 4 | 1 | no | — |
| 131 | D4×C71 | — | 8 | 2 | no | — |
| 132 | C2×C4×C71 | — | 2 | 1 | no | — |
| 133 | C2×C4×C71 | — | 2 | 1 | no | — |
| 134 | C2×C4×C71 | — | 8 | 1 | no | — |
| 135 | C2×C4×C71 | C2×C22⋊C4 | 1 | 1 | yes | characteristic |
| 136 | C22⋊D71 | — | 8 | 4 | no | — |
| 137 | C22⋊D71 | — | 8 | 2 | no | — |
| 138 | C22⋊D71 | — | 8 | 1 | no | — |
| 139 | C22⋊D71 | — | 8 | 1 | no | — |
| 140 | C22⋊D71 | — | 8 | 1 | no | — |
| 141 | C2×Dic71 | — | 2 | 1 | no | — |
| 142 | C2×Dic71 | — | 2 | 1 | no | — |
| 143 | C2×Dic71 | — | 4 | 1 | no | — |
| 144 | C2×Dic71 | — | 4 | 1 | no | — |
| 145 | C2×Dic71 | — | 8 | 1 | no | — |
| 146 | C2×Dic71 | #99 | 1 | 1 | yes | characteristic |
| 147 | D284 | — | 4 | 1 | no | — |
| 148 | D284 | — | 4 | 1 | no | — |
| 149 | D284 | — | 4 | 1 | no | — |
| 150 | D284 | — | 8 | 1 | no | — |
| 151 | D284 | — | 8 | 2 | no | — |
| 152 | C4×D71 | — | 2 | 1 | no | — |
| 153 | C4×D71 | — | 2 | 1 | no | — |
| 154 | C4×D71 | — | 4 | 2 | no | — |
| 155 | C4×D71 | — | 4 | 1 | no | — |
| 156 | C4×D71 | — | 4 | 1 | no | — |
| 157 | Dic142 | — | 4 | 1 | no | — |
| 158 | C8×C71 | — | 2 | 2 | no | — |
| 159 | C8×C71 | — | 8 | 1 | no | — |
| 160 | C71⋊C8 | — | 2 | 2 | no | — |
| 161 | C71⋊C8 | — | 8 | 1 | no | — |
| 162 | C22×C71 | — | 4 | 1 | no | — |
| 163 | C22×C71 | — | 8 | 1 | no | — |
| 164 | C22×C71 | — | 8 | 2 | no | — |
| 165 | C22×C71 | — | 8 | 1 | no | — |
| 166 | C22×C71 | C2×#99 | 1 | 1 | yes | characteristic |
| 167 | C2×D71 | — | 2 | 1 | no | — |
| 168 | C2×D71 | — | 4 | 1 | no | — |
| 169 | C2×D71 | — | 4 | 1 | no | — |
| 170 | C2×D71 | — | 8 | 1 | no | — |
| 171 | C2×D71 | — | 8 | 2 | no | — |
| 172 | C2×D71 | — | 8 | 1 | no | — |
| 173 | C2×D71 | — | 16 | 2 | no | — |
| 174 | C2×D71 | — | 16 | 2 | no | — |
| 175 | C4×C71 | — | 2 | 1 | no | — |
| 176 | C4×C71 | — | 4 | 1 | no | — |
| 177 | C4×C71 | — | 4 | 1 | no | — |
| 178 | C4×C71 | — | 16 | 1 | no | — |
| 179 | Dic71 | — | 2 | 2 | no | — |
| 180 | Dic71 | — | 4 | 1 | no | — |
| 181 | Dic71 | — | 16 | 1 | no | — |
| 182 | Dic71 | #353 | 1 | 1 | yes | characteristic |
| 183 | Dic71 | #353 | 1 | 1 | yes | characteristic |
| 184 | #13579 | — | 71 | 1 | no | maximal, Sylow |
| 185 | C2×C71 | — | 2 | 1 | no | — |
| 186 | C2×C71 | — | 8 | 1 | no | — |
| 187 | C2×C71 | — | 16 | 1 | no | — |
| 188 | C2×C71 | C2×#353 | 1 | 1 | yes | characteristic |
| 189 | D71 | — | 4 | 1 | no | — |
| 190 | D71 | — | 8 | 1 | no | — |
| 191 | D71 | — | 16 | 1 | no | — |
| 192 | #3151 | — | 71 | 1 | no | — |
| 193 | #2132 | — | 71 | 1 | no | — |
| 194 | #2126 | — | 71 | 1 | no | — |
| 195 | #1406 | — | 71 | 1 | no | — |
| 196 | #1406 | — | 71 | 1 | no | — |
| 197 | #1406 | — | 71 | 1 | no | — |
| 198 | #1406 | D71 | 1 | 1 | yes | characteristic, complemented |
| 199 | C71 | #13579 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 200 | C2×AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 201 | C2×AGL(1,ℤ/8) | — | 142 | 1 | no | — |
| 202 | #532 | — | 71 | 1 | no | — |
| 203 | C2×#127 | — | 71 | 1 | no | — |
| 204 | #496 | — | 71 | 1 | no | — |
| 205 | #496 | — | 71 | 1 | no | — |
| 206 | #496 | — | 71 | 1 | no | — |
| 207 | #496 | C2×D71 | 1 | 1 | yes | characteristic |
| 208 | #493 | — | 142 | 1 | no | — |
| 209 | #492 | — | 142 | 1 | no | — |
| 210 | #413 | — | 142 | 1 | no | — |
| 211 | #410 | — | 142 | 1 | no | — |
| 212 | C4×M16 | — | 71 | 1 | no | — |
| 213 | #356 | — | 142 | 1 | no | — |
| 214 | #355 | — | 71 | 1 | no | — |
| 215 | #355 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 216 | #354 | — | 71 | 1 | no | — |
| 217 | #354 | C2×D71 | 1 | 1 | yes | characteristic, complemented |
| 218 | #353 | — | 142 | 1 | no | — |
| 219 | C2×#41 | — | 71 | 1 | no | — |
| 220 | C2×#41 | — | 71 | 1 | no | — |
| 221 | C22×D4 | — | 284 | 1 | no | — |
| 222 | C22×D4 | — | 142 | 1 | no | — |
| 223 | AGL(1,ℤ/8) | — | 284 | 2 | no | — |
| 224 | AGL(1,ℤ/8) | — | 284 | 2 | no | — |
| 225 | AGL(1,ℤ/8) | — | 284 | 2 | no | — |
| 226 | AGL(1,ℤ/8) | — | 284 | 2 | no | — |
| 227 | C2×SD16 | — | 2 | 1 | no | — |
| 228 | C2×SD16 | — | 142 | 1 | no | — |
| 229 | C2×SD16 | — | 142 | 1 | no | — |
| 230 | C2×SD16 | — | 142 | 1 | no | — |
| 231 | C2×D8 | — | 2 | 1 | no | — |
| 232 | C2×D8 | — | 142 | 1 | no | — |
| 233 | C2×D8 | — | 142 | 1 | no | — |
| 234 | C2×D8 | — | 142 | 1 | no | — |
| 235 | C2×M16 | — | 284 | 1 | no | — |
| 236 | C2×M16 | — | 142 | 1 | no | — |
| 237 | C4⋊Q8 | — | 71 | 1 | no | — |
| 238 | #127 | — | 284 | 1 | no | — |
| 239 | #127 | — | 71 | 1 | no | — |
| 240 | #127 | — | 71 | 1 | no | — |
| 241 | #127 | — | 142 | 1 | no | — |
| 242 | #127 | C4×D71 | 1 | 1 | yes | characteristic |
| 243 | #124 | — | 71 | 1 | no | — |
| 244 | #124 | C22×D71 | 1 | 1 | yes | characteristic |
| 245 | #121 | — | 284 | 1 | no | — |
| 246 | C4×D4 | — | 284 | 1 | no | — |
| 247 | #117 | — | 284 | 1 | no | — |
| 248 | C2×C42 | — | 71 | 1 | no | — |
| 249 | #101 | — | 2 | 1 | no | — |
| 250 | #101 | — | 142 | 1 | no | — |
| 251 | #100 | — | 284 | 1 | no | — |
| 252 | #99 | — | 2 | 1 | no | — |
| 253 | #99 | — | 284 | 1 | no | — |
| 254 | #99 | — | 142 | 1 | no | — |
| 255 | #97 | — | 71 | 1 | no | — |
| 256 | #97 | C4×D71 | 1 | 1 | yes | characteristic |
| 257 | C4×C8 | — | 142 | 1 | no | — |
| 258 | C24 | — | 284 | 1 | no | — |
| 259 | #41 | — | 284 | 1 | no | — |
| 260 | #41 | — | 284 | 1 | no | — |
| 261 | #41 | — | 284 | 1 | no | — |
| 262 | #41 | — | 284 | 1 | no | — |
| 263 | C2×Q8 | — | 71 | 1 | no | — |
| 264 | C2×Q8 | D4×D71 | 1 | 1 | yes | characteristic |
| 265 | C2×D4 | — | 2 | 1 | no | — |
| 266 | C2×D4 | — | 4 | 1 | no | — |
| 267 | C2×D4 | — | 284 | 1 | no | — |
| 268 | C2×D4 | — | 284 | 1 | no | — |
| 269 | C2×D4 | — | 284 | 1 | no | — |
| 270 | C2×D4 | — | 284 | 1 | no | — |
| 271 | C2×D4 | — | 284 | 1 | no | — |
| 272 | C2×D4 | — | 284 | 1 | no | — |
| 273 | C2×D4 | — | 284 | 1 | no | — |
| 274 | C2×D4 | — | 284 | 2 | no | — |
| 275 | C2×D4 | — | 568 | 4 | no | — |
| 276 | C2×D4 | — | 71 | 1 | no | — |
| 277 | C2×D4 | — | 142 | 1 | no | — |
| 278 | C2×D4 | — | 142 | 1 | no | — |
| 279 | C2×D4 | — | 142 | 1 | no | — |
| 280 | C2×D4 | D4×D71 | 1 | 1 | yes | characteristic |
| 281 | C22×C4 | — | 71 | 1 | no | — |
| 282 | C22×C4 | — | 142 | 1 | no | — |
| 283 | C22×C4 | — | 142 | 1 | no | — |
| 284 | C22×C4 | — | 142 | 1 | no | — |
| 285 | SD16 | — | 4 | 2 | no | — |
| 286 | SD16 | — | 284 | 2 | no | — |
| 287 | SD16 | — | 284 | 2 | no | — |
| 288 | SD16 | — | 284 | 2 | no | — |
| 289 | D8 | — | 4 | 2 | no | — |
| 290 | D8 | — | 284 | 2 | no | — |
| 291 | D8 | — | 284 | 2 | no | — |
| 292 | D8 | — | 284 | 2 | no | — |
| 293 | M16 | — | 4 | 1 | no | — |
| 294 | M16 | — | 284 | 1 | no | — |
| 295 | M16 | — | 568 | 1 | no | — |
| 296 | M16 | — | 142 | 2 | no | — |
| 297 | M16 | — | 142 | 2 | no | — |
| 298 | C2×C8 | — | 2 | 1 | no | — |
| 299 | C2×C8 | — | 568 | 1 | no | — |
| 300 | C2×C8 | — | 142 | 1 | no | — |
| 301 | C4⋊C4 | — | 284 | 1 | no | — |
| 302 | C4⋊C4 | — | 568 | 1 | no | — |
| 303 | C22⋊C4 | — | 4 | 1 | no | — |
| 304 | C22⋊C4 | — | 4 | 1 | no | — |
| 305 | C22⋊C4 | — | 284 | 1 | no | — |
| 306 | C22⋊C4 | — | 284 | 1 | no | — |
| 307 | C42 | — | 568 | 1 | no | — |
| 308 | C42 | — | 71 | 1 | no | — |
| 309 | C42 | — | 142 | 1 | no | — |
| 310 | C42 | C2×C4×D71 | 1 | 1 | yes | characteristic |
| 311 | C23 | — | 2 | 1 | no | — |
| 312 | C23 | — | 4 | 1 | no | — |
| 313 | C23 | — | 284 | 1 | no | — |
| 314 | C23 | — | 568 | 4 | no | — |
| 315 | C23 | — | 568 | 1 | no | — |
| 316 | C23 | — | 568 | 1 | no | — |
| 317 | C23 | — | 71 | 1 | no | — |
| 318 | C23 | — | 142 | 1 | no | — |
| 319 | Q8 | — | 4 | 1 | no | — |
| 320 | Q8 | — | 284 | 1 | no | — |
| 321 | D4 | — | 4 | 1 | no | — |
| 322 | D4 | — | 4 | 1 | no | — |
| 323 | D4 | — | 4 | 1 | no | — |
| 324 | D4 | — | 8 | 2 | no | — |
| 325 | D4 | — | 284 | 1 | no | — |
| 326 | D4 | — | 284 | 1 | no | — |
| 327 | D4 | — | 284 | 1 | no | — |
| 328 | D4 | — | 568 | 1 | no | — |
| 329 | D4 | — | 568 | 2 | no | — |
| 330 | D4 | — | 568 | 1 | no | — |
| 331 | D4 | — | 568 | 1 | no | — |
| 332 | D4 | — | 568 | 1 | no | — |
| 333 | D4 | — | 568 | 4 | no | — |
| 334 | D4 | — | 568 | 2 | no | — |
| 335 | C2×C4 | — | 2 | 1 | no | — |
| 336 | C2×C4 | — | 2 | 1 | no | — |
| 337 | C2×C4 | — | 8 | 1 | no | — |
| 338 | C2×C4 | — | 284 | 1 | no | — |
| 339 | C2×C4 | — | 284 | 1 | no | — |
| 340 | C2×C4 | — | 284 | 2 | no | — |
| 341 | C2×C4 | — | 284 | 1 | no | — |
| 342 | C2×C4 | — | 284 | 1 | no | — |
| 343 | C2×C4 | — | 568 | 1 | no | — |
| 344 | C2×C4 | — | 71 | 1 | no | — |
| 345 | C2×C4 | — | 142 | 1 | no | — |
| 346 | C2×C4 | — | 142 | 1 | no | — |
| 347 | C2×C4 | — | 142 | 1 | no | — |
| 348 | C2×C4 | — | 142 | 1 | no | — |
| 349 | C2×C4 | C22⋊C4×D71 | 1 | 1 | yes | characteristic |
| 350 | C8 | — | 2 | 2 | no | — |
| 351 | C8 | — | 8 | 1 | no | — |
| 352 | C8 | — | 568 | 1 | no | — |
| 353 | C8 | — | 142 | 2 | no | — |
| 354 | C22 | — | 4 | 1 | no | — |
| 355 | C22 | — | 8 | 1 | no | — |
| 356 | C22 | — | 8 | 2 | no | — |
| 357 | C22 | — | 8 | 1 | no | — |
| 358 | C22 | — | 284 | 1 | no | — |
| 359 | C22 | — | 284 | 1 | no | — |
| 360 | C22 | — | 568 | 1 | no | — |
| 361 | C22 | — | 568 | 2 | no | — |
| 362 | C22 | — | 568 | 1 | no | — |
| 363 | C22 | — | 1136 | 2 | no | — |
| 364 | C22 | — | 1136 | 2 | no | — |
| 365 | C22 | — | 142 | 1 | no | — |
| 366 | C22 | #99×D71 | 1 | 1 | yes | characteristic |
| 367 | C4 | — | 2 | 1 | no | — |
| 368 | C4 | — | 4 | 1 | no | — |
| 369 | C4 | — | 4 | 1 | no | — |
| 370 | C4 | — | 16 | 1 | no | — |
| 371 | C4 | — | 284 | 1 | no | — |
| 372 | C4 | — | 71 | 1 | no | — |
| 373 | C4 | — | 71 | 1 | no | — |
| 374 | C4 | — | 1136 | 1 | no | — |
| 375 | C4 | — | 142 | 2 | no | — |
| 376 | C2 | — | 2 | 1 | no | — |
| 377 | C2 | — | 8 | 1 | no | — |
| 378 | C2 | — | 16 | 1 | no | — |
| 379 | C2 | — | 284 | 1 | no | — |
| 380 | C2 | — | 568 | 1 | no | — |
| 381 | C2 | — | 1136 | 1 | no | — |
| 382 | C2 | #353×D71 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22590022 | C2 | semidirect |
| 3. #22590004 | C2 | semidirect |
| 4. #22586498 | C2 | semidirect |
| 5. #22586497 | C2 | semidirect |
| 6. #22586496 | C2 | semidirect |
| 7. C71×#1406 | C2 | semidirect |
| 11. #127×D71 | C4 | semidirect |
| 13. #17986388 | C4 | semidirect |
| 14. #17986386 | C4 | semidirect |
| 19. #17985951 | C4 | semidirect |
| 21. #17985796 | C22 | semidirect |
| 22. #17985794 | C22 | semidirect |
| 25. #355×C71 | C22 | semidirect |
| 26. #354×C71 | C22 | semidirect |
| 198. #1406 | D71 | semidirect |
| 199. C71 | #13579 | semidirect |
| 215. #355 | C2×D71 | semidirect |
| 217. #354 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22598789 | 2 |
| #22590022 | 2 |
| #22590004 | 2 |
| #22586498 | 2 |
| #22586497 | 2 |
| #22586496 | 2 |
| C71×#1406 | 2 |
| #13579 | 71 |