Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
1270 conjugacy classes of subgroups; only the 231 normal subgroups are shown.
This group has 1270 conjugacy classes of subgroups — too many to draw. Only its 231 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 | #22601985 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #22596816 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #22588891 | C2 | 1 | 4 | yes | maximal, complemented |
| 4 | #22588757 | C2 | 1 | 4 | yes | maximal, complemented |
| 5 | #22588451 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #22588265 | C2 | 1 | 2 | yes | maximal, complemented |
| 7 | C71×#1829 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C2×#14556173 | C22 | 1 | 1 | yes | characteristic |
| 9 | C22×#11765864 | C22 | 1 | 1 | yes | characteristic |
| 10 | #17986765 | C22 | 1 | 4 | yes | — |
| 11 | #17986653 | — | 2 | 4 | no | — |
| 12 | #17986644 | — | 2 | 4 | no | — |
| 13 | #17986575 | C22 | 1 | 2 | yes | — |
| 14 | #17986561 | C4 | 1 | 4 | yes | — |
| 15 | #17986511 | C22 | 1 | 2 | yes | — |
| 16 | C2×#14556112 | C4 | 1 | 4 | yes | — |
| 17 | #17985981 | C22 | 1 | 4 | yes | — |
| 18 | #17985980 | — | 2 | 4 | no | — |
| 19 | C2×#14556046 | C22 | 1 | 4 | yes | complemented |
| 20 | C2×#14556045 | C22 | 1 | 2 | yes | — |
| 21 | #100×D71 | — | 2 | 4 | no | — |
| 22 | #17985962 | C22 | 1 | 4 | yes | complemented |
| 23 | #17985769 | C22 | 1 | 4 | yes | complemented |
| 24 | #518×C71 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×#100×C71 | C22 | 1 | 2 | yes | — |
| 26 | #344×C71 | C22 | 1 | 4 | yes | complemented |
| 27 | #14556173 | — | 4 | 4 | no | — |
| 28 | C2×#11765865 | C23 | 1 | 2 | yes | — |
| 29 | C2×#11765864 | — | 2 | 4 | no | — |
| 30 | C2×#11765864 | — | 4 | 4 | no | — |
| 31 | C2×#11765864 | D4 | 1 | 4 | yes | — |
| 32 | C22×Dic142 | C23 | 1 | 1 | yes | characteristic |
| 33 | C22×C22⋊D71 | C2×C4 | 1 | 4 | yes | — |
| 34 | C22×C22⋊D71 | C2×C4 | 1 | 2 | yes | — |
| 35 | C2×D4×D71 | D4 | 1 | 4 | yes | — |
| 36 | C23×Dic71 | C2×C4 | 1 | 2 | yes | — |
| 37 | C22×C4×D71 | C23 | 1 | 1 | yes | characteristic |
| 38 | #14556136 | — | 4 | 4 | no | — |
| 39 | #14556134 | — | 4 | 4 | no | — |
| 40 | C2×#11765849 | C23 | 1 | 4 | yes | — |
| 41 | M16×D71 | — | 2 | 8 | no | — |
| 42 | #14556128 | — | 2 | 2 | no | — |
| 43 | #14556116 | — | 2 | 2 | no | — |
| 44 | #14556112 | — | 2 | 8 | no | — |
| 45 | #14556112 | — | 2 | 4 | no | — |
| 46 | #14556112 | C2×C4 | 1 | 8 | yes | — |
| 47 | #14556112 | C2×C4 | 1 | 4 | yes | — |
| 48 | #14556108 | — | 2 | 2 | no | — |
| 49 | #14556108 | — | 2 | 4 | no | — |
| 50 | #14556103 | — | 2 | 2 | no | — |
| 51 | #14556102 | — | 2 | 8 | no | — |
| 52 | #14556098 | — | 2 | 4 | no | — |
| 53 | #14556098 | C2×C4 | 1 | 4 | yes | — |
| 54 | C4×D284 | — | 2 | 4 | no | — |
| 55 | C2×C4⋊Dic71 | — | 2 | 4 | no | — |
| 56 | C2×(C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 57 | #14556046 | — | 2 | 4 | no | — |
| 58 | #14556046 | — | 4 | 4 | no | — |
| 59 | #14556045 | — | 2 | 4 | no | — |
| 60 | #14556044 | — | 2 | 4 | no | — |
| 61 | (C2×D71)⋊C8 | — | 4 | 4 | no | — |
| 62 | C22×D4×C71 | C23 | 1 | 1 | yes | characteristic |
| 63 | C2×M16×C71 | C23 | 1 | 4 | yes | — |
| 64 | C4×D4×C71 | — | 2 | 4 | no | — |
| 65 | #117×C71 | C23 | 1 | 2 | yes | — |
| 66 | C2×C22⋊C4×C71 | C2×C4 | 1 | 4 | yes | — |
| 67 | #100×C71 | — | 2 | 4 | no | — |
| 68 | C23×D71 | C22⋊C4 | 1 | 4 | yes | — |
| 69 | C23×D71 | C22×C4 | 1 | 1 | yes | characteristic |
| 70 | #11765865 | — | 2 | 4 | no | — |
| 71 | #11765865 | — | 2 | 4 | no | — |
| 72 | #11765864 | — | 4 | 8 | no | — |
| 73 | #11765864 | — | 4 | 16 | no | — |
| 74 | C2×Dic142 | — | 2 | 2 | no | — |
| 75 | C2×Dic142 | — | 2 | 4 | no | — |
| 76 | C2×Dic142 | C2×D4 | 1 | 2 | yes | — |
| 77 | C2×D284 | — | 2 | 4 | no | — |
| 78 | C2×D284 | C2×D4 | 1 | 2 | yes | — |
| 79 | C2×C22⋊D71 | — | 2 | 4 | no | — |
| 80 | C2×C22⋊D71 | — | 4 | 4 | no | — |
| 81 | C2×C22⋊D71 | — | 4 | 8 | no | — |
| 82 | C2×C22⋊D71 | C22⋊C4 | 1 | 8 | yes | — |
| 83 | C2×C22⋊D71 | C22×C4 | 1 | 4 | yes | — |
| 84 | D4×D71 | — | 4 | 8 | no | — |
| 85 | C22×Dic71 | — | 2 | 4 | no | — |
| 86 | C22×Dic71 | — | 4 | 4 | no | — |
| 87 | C22×Dic71 | C22⋊C4 | 1 | 4 | yes | — |
| 88 | C22×Dic71 | C22×C4 | 1 | 1 | yes | characteristic |
| 89 | C22×Dic71 | C22×C4 | 1 | 2 | yes | — |
| 90 | C2×C4×D71 | — | 2 | 2 | no | — |
| 91 | C2×C4×D71 | — | 2 | 4 | no | — |
| 92 | C2×C4×D71 | C2×D4 | 1 | 4 | yes | — |
| 93 | #11765849 | — | 2 | 4 | no | — |
| 94 | #11765849 | — | 2 | 4 | no | — |
| 95 | #11765848 | — | 4 | 8 | no | — |
| 96 | C2×C71⋊C8 | — | 2 | 4 | no | — |
| 97 | C8×D71 | — | 4 | 8 | no | — |
| 98 | C4⋊Dic71 | — | 2 | 4 | no | — |
| 99 | C4⋊Dic71 | — | 2 | 8 | no | — |
| 100 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 101 | (C2×D71)⋊C4 | — | 2 | 8 | no | — |
| 102 | (C2×D71)⋊C4 | — | 2 | 4 | no | — |
| 103 | C24×C71 | C22×C4 | 1 | 2 | yes | — |
| 104 | C2×D4×C71 | — | 2 | 4 | no | — |
| 105 | C2×D4×C71 | C2×D4 | 1 | 4 | yes | — |
| 106 | C22×C4×C71 | — | 2 | 4 | no | — |
| 107 | C22×C4×C71 | C24 | 1 | 1 | yes | characteristic |
| 108 | M16×C71 | — | 2 | 4 | no | — |
| 109 | M16×C71 | — | 2 | 4 | no | — |
| 110 | C2×C8×C71 | — | 2 | 4 | no | — |
| 111 | C4⋊C4×C71 | — | 2 | 2 | no | — |
| 112 | C22⋊C4×C71 | — | 2 | 4 | no | — |
| 113 | C22⋊C4×C71 | C22×C4 | 1 | 4 | yes | — |
| 114 | C42×C71 | — | 2 | 2 | no | — |
| 115 | C23×C71 | — | 2 | 4 | no | — |
| 116 | C23×C71 | — | 8 | 2 | no | — |
| 117 | C23×C71 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 118 | C23×C71 | C23×C4 | 1 | 1 | yes | characteristic |
| 119 | C22×D71 | — | 2 | 1 | no | — |
| 120 | C22×D71 | — | 2 | 2 | no | — |
| 121 | C22×D71 | — | 4 | 4 | no | — |
| 122 | C22×D71 | — | 8 | 1 | no | — |
| 123 | C22×D71 | — | 8 | 4 | no | — |
| 124 | C22×D71 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 125 | D4×C71 | — | 2 | 8 | no | — |
| 126 | C2×C4×C71 | — | 2 | 4 | no | — |
| 127 | C2×C4×C71 | — | 8 | 4 | no | — |
| 128 | C2×C4×C71 | C22×D4 | 1 | 2 | yes | — |
| 129 | C2×C4×C71 | H(5,𝔽2) | 1 | 4 | yes | — |
| 130 | C22⋊D71 | — | 2 | 4 | no | — |
| 131 | C22⋊D71 | — | 2 | 4 | no | — |
| 132 | C22⋊D71 | — | 4 | 8 | no | — |
| 133 | C22⋊D71 | — | 4 | 8 | no | — |
| 134 | C2×Dic71 | — | 2 | 1 | no | — |
| 135 | C2×Dic71 | — | 2 | 2 | no | — |
| 136 | C2×Dic71 | — | 2 | 2 | no | — |
| 137 | C2×Dic71 | — | 2 | 4 | no | — |
| 138 | C2×Dic71 | — | 4 | 4 | no | — |
| 139 | C2×Dic71 | — | 4 | 8 | no | — |
| 140 | C2×Dic71 | C2×C22⋊C4 | 1 | 4 | yes | — |
| 141 | D284 | — | 2 | 4 | no | — |
| 142 | D284 | — | 8 | 4 | no | — |
| 143 | C4×D71 | — | 2 | 8 | no | — |
| 144 | C4×D71 | — | 4 | 4 | no | — |
| 145 | Dic142 | — | 2 | 4 | no | — |
| 146 | Dic142 | — | 4 | 4 | no | — |
| 147 | C8×C71 | — | 4 | 4 | no | — |
| 148 | C71⋊C8 | — | 4 | 4 | no | — |
| 149 | C22×C71 | — | 2 | 4 | no | — |
| 150 | C22×C71 | — | 4 | 1 | no | — |
| 151 | C22×C71 | — | 4 | 4 | no | — |
| 152 | C22×C71 | — | 8 | 4 | no | — |
| 153 | C22×C71 | C22×C22⋊C4 | 1 | 1 | yes | characteristic |
| 154 | C22×C71 | #518 | 1 | 2 | yes | — |
| 155 | C2×D71 | — | 2 | 4 | no | — |
| 156 | C2×D71 | — | 4 | 4 | no | — |
| 157 | C2×D71 | — | 4 | 2 | no | — |
| 158 | C2×D71 | — | 4 | 4 | no | — |
| 159 | C2×D71 | — | 4 | 1 | no | — |
| 160 | C2×D71 | — | 16 | 4 | no | — |
| 161 | C4×C71 | — | 4 | 4 | no | — |
| 162 | C4×C71 | #534 | 1 | 4 | yes | — |
| 163 | Dic71 | — | 2 | 4 | no | — |
| 164 | Dic71 | — | 4 | 2 | no | — |
| 165 | Dic71 | — | 4 | 1 | no | — |
| 166 | #21779 | — | 71 | 1 | no | maximal, Sylow |
| 167 | C2×C71 | — | 2 | 1 | no | — |
| 168 | C2×C71 | — | 2 | 2 | no | — |
| 169 | C2×C71 | — | 4 | 4 | no | — |
| 170 | C2×C71 | #2308 | 1 | 1 | yes | characteristic |
| 171 | D71 | — | 4 | 4 | no | — |
| 172 | D71 | — | 8 | 1 | no | — |
| 173 | #3485 | — | 71 | 1 | no | — |
| 174 | #2888 | — | 71 | 2 | no | — |
| 175 | #1915 | — | 71 | 4 | no | — |
| 176 | #1891 | — | 71 | 4 | no | — |
| 177 | #1829 | — | 71 | 1 | no | — |
| 178 | #1829 | D71 | 1 | 1 | yes | characteristic, complemented |
| 179 | #1785 | — | 71 | 2 | no | — |
| 180 | C71 | #21779 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 181 | C2×H(5,𝔽2) | — | 71 | 1 | no | — |
| 182 | C22×#41 | — | 71 | 1 | no | — |
| 183 | #568 | — | 71 | 4 | no | — |
| 184 | #547 | — | 142 | 4 | no | — |
| 185 | #546 | — | 142 | 4 | no | — |
| 186 | #536 | — | 71 | 2 | no | — |
| 187 | #534 | — | 71 | 4 | no | — |
| 188 | #525 | — | 71 | 2 | no | — |
| 189 | C2×#123 | — | 71 | 4 | no | — |
| 190 | #518 | C2×D71 | 1 | 1 | yes | characteristic |
| 191 | #413 | — | 71 | 4 | no | — |
| 192 | #413 | — | 142 | 4 | no | — |
| 193 | C2×#101 | — | 71 | 4 | no | — |
| 194 | C2×#100 | — | 71 | 2 | no | — |
| 195 | C2×#100 | — | 142 | 4 | no | — |
| 196 | C2×#100 | C2×D71 | 1 | 2 | yes | — |
| 197 | #407 | — | 71 | 4 | no | — |
| 198 | #344 | — | 71 | 4 | no | — |
| 199 | #344 | C2×D71 | 1 | 4 | yes | complemented |
| 200 | H(5,𝔽2) | — | 284 | 4 | no | — |
| 201 | C2×#41 | — | 284 | 4 | no | — |
| 202 | C2×#41 | — | 71 | 4 | no | — |
| 203 | C2×#41 | — | 71 | 2 | no | — |
| 204 | C2×#41 | — | 142 | 4 | no | — |
| 205 | C22×Q8 | — | 71 | 1 | no | — |
| 206 | C22×D4 | — | 71 | 4 | no | — |
| 207 | C22×D4 | — | 71 | 4 | no | — |
| 208 | C22×D4 | — | 71 | 2 | no | — |
| 209 | C22×D4 | C22×D71 | 1 | 1 | yes | characteristic |
| 210 | C23×C4 | — | 71 | 2 | no | — |
| 211 | C23×C4 | — | 71 | 1 | no | — |
| 212 | #131 | — | 284 | 4 | no | — |
| 213 | #131 | — | 284 | 4 | no | — |
| 214 | C2×M16 | — | 71 | 4 | no | — |
| 215 | C2×M16 | — | 142 | 8 | no | — |
| 216 | C2×M16 | C22×D71 | 1 | 4 | yes | — |
| 217 | C4⋊Q8 | — | 142 | 2 | no | — |
| 218 | #124 | — | 142 | 2 | no | — |
| 219 | #123 | — | 71 | 4 | no | — |
| 220 | #123 | — | 71 | 8 | no | — |
| 221 | #123 | — | 142 | 4 | no | — |
| 222 | #123 | — | 142 | 8 | no | — |
| 223 | C22⋊Q8 | — | 142 | 4 | no | — |
| 224 | C22⋊Q8 | — | 142 | 2 | no | — |
| 225 | #121 | — | 142 | 2 | no | — |
| 226 | #121 | — | 142 | 8 | no | — |
| 227 | #120 | — | 71 | 4 | no | — |
| 228 | #120 | — | 142 | 4 | no | — |
| 229 | C4×D4 | — | 2 | 4 | no | — |
| 230 | C4×D4 | — | 142 | 4 | no | — |
| 231 | #117 | C22×D71 | 1 | 2 | yes | — |
| 232 | C2×C4⋊C4 | — | 142 | 4 | no | — |
| 233 | C2×C22⋊C4 | — | 142 | 4 | no | — |
| 234 | C2×C22⋊C4 | C4×D71 | 1 | 4 | yes | — |
| 235 | #101 | — | 284 | 4 | no | — |
| 236 | #101 | — | 142 | 4 | no | — |
| 237 | #100 | — | 2 | 4 | no | — |
| 238 | #100 | — | 142 | 4 | no | — |
| 239 | #100 | — | 142 | 4 | no | — |
| 240 | C22⋊C8 | — | 284 | 4 | no | — |
| 241 | C24 | — | 71 | 4 | no | — |
| 242 | C24 | — | 71 | 1 | no | — |
| 243 | C24 | C2×C4×D71 | 1 | 2 | yes | — |
| 244 | #41 | — | 284 | 16 | no | — |
| 245 | #41 | — | 284 | 8 | no | — |
| 246 | #41 | — | 142 | 4 | no | — |
| 247 | #41 | — | 142 | 4 | no | — |
| 248 | C2×Q8 | — | 71 | 2 | no | — |
| 249 | C2×Q8 | — | 142 | 2 | no | — |
| 250 | C2×Q8 | — | 142 | 4 | no | — |
| 251 | C2×D4 | — | 2 | 4 | no | — |
| 252 | C2×D4 | — | 284 | 8 | no | — |
| 253 | C2×D4 | — | 284 | 8 | no | — |
| 254 | C2×D4 | — | 284 | 4 | no | — |
| 255 | C2×D4 | — | 71 | 8 | no | — |
| 256 | C2×D4 | — | 71 | 4 | no | — |
| 257 | C2×D4 | — | 71 | 2 | no | — |
| 258 | C2×D4 | — | 142 | 4 | no | — |
| 259 | C2×D4 | — | 142 | 4 | no | — |
| 260 | C2×D4 | D4×D71 | 1 | 4 | yes | — |
| 261 | C22×C4 | — | 2 | 4 | no | — |
| 262 | C22×C4 | — | 284 | 4 | no | — |
| 263 | C22×C4 | — | 71 | 4 | no | — |
| 264 | C22×C4 | — | 71 | 4 | no | — |
| 265 | C22×C4 | — | 71 | 1 | no | — |
| 266 | C22×C4 | — | 71 | 2 | no | — |
| 267 | C22×C4 | — | 142 | 4 | no | — |
| 268 | C22×C4 | — | 142 | 2 | no | — |
| 269 | C22×C4 | — | 142 | 4 | no | — |
| 270 | C22×C4 | C23×D71 | 1 | 1 | yes | characteristic |
| 271 | M16 | — | 2 | 4 | no | — |
| 272 | M16 | — | 2 | 4 | no | — |
| 273 | M16 | — | 284 | 8 | no | — |
| 274 | M16 | — | 142 | 4 | no | — |
| 275 | M16 | — | 142 | 4 | no | — |
| 276 | C2×C8 | — | 2 | 4 | no | — |
| 277 | C2×C8 | — | 284 | 8 | no | — |
| 278 | C2×C8 | — | 142 | 4 | no | — |
| 279 | C4⋊C4 | — | 2 | 2 | no | — |
| 280 | C4⋊C4 | — | 142 | 4 | no | — |
| 281 | C4⋊C4 | — | 142 | 8 | no | — |
| 282 | C22⋊C4 | — | 2 | 4 | no | — |
| 283 | C22⋊C4 | — | 142 | 4 | no | — |
| 284 | C22⋊C4 | — | 142 | 4 | no | — |
| 285 | C22⋊C4 | — | 142 | 8 | no | — |
| 286 | C22⋊C4 | C2×C4×D71 | 1 | 4 | yes | — |
| 287 | C42 | — | 2 | 2 | no | — |
| 288 | C23 | — | 2 | 4 | no | — |
| 289 | C23 | — | 8 | 2 | no | — |
| 290 | C23 | — | 284 | 4 | no | — |
| 291 | C23 | — | 568 | 1 | no | — |
| 292 | C23 | — | 568 | 4 | no | — |
| 293 | C23 | — | 71 | 4 | no | — |
| 294 | C23 | — | 142 | 1 | no | — |
| 295 | C23 | — | 142 | 2 | no | — |
| 296 | C23 | C22⋊C4×D71 | 1 | 4 | yes | — |
| 297 | C23 | C22×C4×D71 | 1 | 1 | yes | characteristic |
| 298 | Q8 | — | 284 | 4 | no | — |
| 299 | Q8 | — | 142 | 4 | no | — |
| 300 | D4 | — | 2 | 8 | no | — |
| 301 | D4 | — | 284 | 8 | no | — |
| 302 | D4 | — | 284 | 8 | no | — |
| 303 | D4 | — | 568 | 4 | no | — |
| 304 | D4 | — | 142 | 4 | no | — |
| 305 | D4 | — | 142 | 4 | no | — |
| 306 | D4 | — | 142 | 4 | no | — |
| 307 | C2×C4 | — | 2 | 4 | no | — |
| 308 | C2×C4 | — | 8 | 4 | no | — |
| 309 | C2×C4 | — | 284 | 8 | no | — |
| 310 | C2×C4 | — | 284 | 4 | no | — |
| 311 | C2×C4 | — | 284 | 4 | no | — |
| 312 | C2×C4 | — | 71 | 4 | no | — |
| 313 | C2×C4 | — | 142 | 1 | no | — |
| 314 | C2×C4 | — | 142 | 2 | no | — |
| 315 | C2×C4 | — | 142 | 2 | no | — |
| 316 | C2×C4 | — | 142 | 4 | no | — |
| 317 | C2×C4 | — | 142 | 8 | no | — |
| 318 | C2×C4 | C2×D4×D71 | 1 | 2 | yes | — |
| 319 | C2×C4 | #14556174 | 1 | 4 | yes | — |
| 320 | C8 | — | 4 | 4 | no | — |
| 321 | C8 | — | 284 | 4 | no | — |
| 322 | C22 | — | 2 | 4 | no | — |
| 323 | C22 | — | 4 | 1 | no | — |
| 324 | C22 | — | 4 | 4 | no | — |
| 325 | C22 | — | 8 | 4 | no | — |
| 326 | C22 | — | 284 | 4 | no | — |
| 327 | C22 | — | 284 | 2 | no | — |
| 328 | C22 | — | 284 | 4 | no | — |
| 329 | C22 | — | 284 | 1 | no | — |
| 330 | C22 | — | 1136 | 4 | no | — |
| 331 | C22 | — | 142 | 4 | no | — |
| 332 | C22 | C2×C22⋊C4×D71 | 1 | 1 | yes | characteristic |
| 333 | C22 | #17986473 | 1 | 2 | yes | — |
| 334 | C4 | — | 4 | 4 | no | — |
| 335 | C4 | — | 284 | 1 | no | — |
| 336 | C4 | — | 284 | 2 | no | — |
| 337 | C4 | — | 142 | 4 | no | — |
| 338 | C4 | #17986560 | 1 | 4 | yes | — |
| 339 | C2 | — | 2 | 1 | no | — |
| 340 | C2 | — | 2 | 2 | no | — |
| 341 | C2 | — | 4 | 4 | no | — |
| 342 | C2 | — | 284 | 4 | no | — |
| 343 | C2 | — | 568 | 1 | no | — |
| 344 | C2 | #22590917 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #22596816 | C2 | semidirect |
| 3. #22588891 | C2 | semidirect |
| 4. #22588757 | C2 | semidirect |
| 5. #22588451 | C2 | semidirect |
| 6. #22588265 | C2 | semidirect |
| 7. C71×#1829 | C2 | semidirect |
| 19. C2×#14556046 | C22 | semidirect |
| 22. #17985962 | C22 | semidirect |
| 23. #17985769 | C22 | semidirect |
| 26. #344×C71 | C22 | semidirect |
| 178. #1829 | D71 | semidirect |
| 180. C71 | #21779 | semidirect |
| 199. #344 | C2×D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601985 | 2 |
| #22596816 | 2 |
| #22588891 | 2 |
| #22588757 | 2 |
| #22588451 | 2 |
| #22588265 | 2 |
| C71×#1829 | 2 |
| #21779 | 71 |