Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
398 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 63 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 | #11738147 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | #11728831 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #11726866 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | #11726618 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | C7×#1347 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #11725330 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #11725291 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | C22×Dic28 | C22 | 1 | 1 | yes | characteristic |
| 9 | #90287 | — | 2 | 1 | no | — |
| 10 | C7×#466 | C22 | 1 | 1 | yes | characteristic |
| 11 | #89922 | — | 2 | 1 | no | — |
| 12 | C2×#6401 | — | 2 | 1 | no | — |
| 13 | #89887 | C22 | 1 | 1 | yes | characteristic |
| 14 | C2×Dic7⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 15 | #89810 | — | 2 | 1 | no | — |
| 16 | #89746 | — | 2 | 1 | no | — |
| 17 | C2×#6384 | — | 2 | 1 | no | — |
| 18 | C2×#6374 | — | 2 | 1 | no | — |
| 19 | #89662 | — | 2 | 1 | no | — |
| 20 | #89558 | — | 2 | 1 | no | — |
| 21 | #89531 | — | 2 | 1 | no | — |
| 22 | C7×C22⋊C16 | C22 | 1 | 1 | yes | characteristic |
| 23 | C7×#340 | C22 | 1 | 1 | yes | characteristic |
| 24 | C22⋊(C7⋊C16) | C22 | 1 | 1 | yes | characteristic |
| 25 | #89298 | — | 2 | 1 | no | — |
| 26 | #89287 | — | 2 | 1 | no | — |
| 27 | #12161 | — | 7 | 1 | no | maximal, Sylow |
| 28 | C2×#1159 | — | 4 | 1 | no | — |
| 29 | C22×Dic14 | — | 2 | 1 | no | — |
| 30 | C2×C7×D8 | D4 | 1 | 1 | yes | characteristic |
| 31 | C22×C7×C8 | C23 | 1 | 1 | yes | characteristic |
| 32 | C7×#121 | — | 2 | 1 | no | — |
| 33 | C2×C7×C4⋊C4 | — | 2 | 1 | no | — |
| 34 | #6503 | — | 2 | 1 | no | — |
| 35 | #6502 | — | 4 | 1 | no | — |
| 36 | D4×Dic7 | — | 2 | 1 | no | — |
| 37 | C2×#1141 | — | 2 | 1 | no | — |
| 38 | #6493 | — | 2 | 1 | no | — |
| 39 | C2×C4×Dic7 | D4 | 1 | 1 | yes | characteristic |
| 40 | C22×C7⋊C8 | D4 | 1 | 1 | yes | characteristic |
| 41 | C2×Dic28 | — | 2 | 1 | no | — |
| 42 | C2×Dic28 | — | 2 | 1 | no | — |
| 43 | C2×Dic28 | — | 4 | 2 | no | — |
| 44 | C2×D56 | D4 | 1 | 1 | yes | characteristic |
| 45 | #6456 | — | 2 | 1 | no | — |
| 46 | #6451 | — | 2 | 1 | no | — |
| 47 | #6448 | — | 4 | 1 | no | — |
| 48 | (C22⋊D7)⋊C4 | — | 4 | 1 | no | — |
| 49 | C2×C7×C16 | — | 2 | 1 | no | — |
| 50 | C7×#107 | D4 | 1 | 1 | yes | characteristic |
| 51 | C7×#102 | — | 2 | 1 | no | — |
| 52 | #6406 | — | 2 | 1 | no | — |
| 53 | C7⋊#95 | — | 4 | 1 | no | — |
| 54 | C7⋊#95 | — | 4 | 1 | no | — |
| 55 | #6401 | — | 4 | 2 | no | — |
| 56 | #6395 | — | 2 | 1 | no | — |
| 57 | #6392 | D4 | 1 | 1 | yes | characteristic |
| 58 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 59 | Dic7⋊C8 | — | 2 | 1 | no | — |
| 60 | C2×C7⋊C16 | — | 2 | 1 | no | — |
| 61 | #6384 | — | 4 | 2 | no | — |
| 62 | #6383 | — | 2 | 1 | no | — |
| 63 | #6381 | — | 2 | 1 | no | — |
| 64 | #6374 | — | 4 | 2 | no | — |
| 65 | #3245 | — | 7 | 1 | no | — |
| 66 | #2185 | — | 7 | 1 | no | — |
| 67 | #2185 | — | 7 | 1 | no | — |
| 68 | #2056 | — | 7 | 1 | no | — |
| 69 | #1347 | — | 7 | 1 | no | — |
| 70 | #1347 | D7 | 1 | 1 | yes | characteristic, complemented |
| 71 | #1322 | — | 7 | 1 | no | — |
| 72 | C2×C7×D4 | — | 2 | 1 | no | — |
| 73 | C2×C7×D4 | — | 4 | 1 | no | — |
| 74 | C22×C4×C7 | — | 4 | 1 | no | — |
| 75 | C22×C4×C7 | C2×D4 | 1 | 1 | yes | characteristic |
| 76 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 77 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 78 | C2×C22⋊D7 | — | 4 | 1 | no | — |
| 79 | C22×Dic7 | — | 4 | 1 | no | — |
| 80 | C22×Dic7 | — | 4 | 1 | no | — |
| 81 | C22×Dic7 | D8 | 1 | 1 | yes | characteristic |
| 82 | C22×Dic7 | D8 | 1 | 1 | yes | characteristic |
| 83 | #1159 | — | 8 | 2 | no | — |
| 84 | #1159 | — | 8 | 2 | no | — |
| 85 | C2×D28 | — | 2 | 1 | no | — |
| 86 | C2×C4×D7 | — | 4 | 1 | no | — |
| 87 | C2×Dic14 | — | 2 | 2 | no | — |
| 88 | C2×Dic14 | — | 4 | 1 | no | — |
| 89 | C2×Dic14 | — | 4 | 1 | no | — |
| 90 | C2×Dic14 | — | 4 | 1 | no | — |
| 91 | C2×Dic14 | — | 4 | 1 | no | — |
| 92 | C2×Dic14 | — | 4 | 1 | no | — |
| 93 | C2×Dic14 | — | 4 | 1 | no | — |
| 94 | C7×D8 | — | 4 | 1 | no | — |
| 95 | C2×C7×C8 | — | 4 | 1 | no | — |
| 96 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 97 | C2×C7×C8 | C2×D4 | 1 | 1 | yes | characteristic |
| 98 | C7×C4⋊C4 | — | 2 | 1 | no | — |
| 99 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 100 | C7×C4⋊C4 | — | 4 | 1 | no | — |
| 101 | C7×C22⋊C4 | — | 4 | 1 | no | — |
| 102 | C22⋊Dic7 | — | 4 | 1 | no | — |
| 103 | #1141 | — | 8 | 1 | no | — |
| 104 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 105 | (C2×D7)⋊C4 | — | 4 | 1 | no | — |
| 106 | C4⋊Dic7 | — | 2 | 1 | no | — |
| 107 | Dic7⋊C4 | — | 4 | 1 | no | — |
| 108 | C4×Dic7 | — | 2 | 1 | no | — |
| 109 | C4×Dic7 | — | 2 | 1 | no | — |
| 110 | C2×C7⋊C8 | — | 2 | 1 | no | — |
| 111 | C2×C7⋊C8 | — | 4 | 1 | no | — |
| 112 | Dic28 | — | 2 | 2 | no | — |
| 113 | Dic28 | — | 2 | 2 | no | — |
| 114 | Dic28 | — | 4 | 1 | no | — |
| 115 | Dic28 | — | 4 | 1 | no | — |
| 116 | D56 | — | 4 | 1 | no | — |
| 117 | C7×C16 | — | 4 | 1 | no | — |
| 118 | C7⋊C16 | — | 4 | 1 | no | — |
| 119 | C22×Q16 | — | 7 | 1 | no | — |
| 120 | #532 | — | 14 | 1 | no | — |
| 121 | C2×SD32 | — | 14 | 1 | no | — |
| 122 | C2×SD32 | — | 14 | 1 | no | — |
| 123 | #474 | — | 14 | 1 | no | — |
| 124 | #474 | — | 14 | 1 | no | — |
| 125 | #466 | — | 7 | 1 | no | — |
| 126 | #466 | — | 14 | 1 | no | — |
| 127 | #466 | C2×D7 | 1 | 1 | yes | characteristic |
| 128 | #459 | — | 14 | 1 | no | — |
| 129 | #459 | — | 14 | 1 | no | — |
| 130 | C2×C4⋊C8 | — | 7 | 1 | no | — |
| 131 | C2×#103 | — | 14 | 1 | no | — |
| 132 | #391 | — | 14 | 1 | no | — |
| 133 | #358 | — | 14 | 1 | no | — |
| 134 | #358 | — | 14 | 1 | no | — |
| 135 | C22⋊C16 | — | 7 | 1 | no | — |
| 136 | C22⋊C16 | C2×D7 | 1 | 1 | yes | characteristic |
| 137 | #340 | C2×D7 | 1 | 1 | yes | characteristic |
| 138 | C23×C7 | — | 4 | 1 | no | — |
| 139 | C23×C7 | C2×D8 | 1 | 1 | yes | characteristic |
| 140 | C22×D7 | — | 4 | 1 | no | — |
| 141 | C7×D4 | — | 4 | 1 | no | — |
| 142 | C7×D4 | — | 4 | 1 | no | — |
| 143 | C7×D4 | — | 8 | 1 | no | — |
| 144 | C7×D4 | — | 8 | 1 | no | — |
| 145 | C2×C4×C7 | — | 2 | 1 | no | — |
| 146 | C2×C4×C7 | — | 2 | 1 | no | — |
| 147 | C2×C4×C7 | — | 4 | 1 | no | — |
| 148 | C2×C4×C7 | — | 8 | 1 | no | — |
| 149 | C2×C4×C7 | — | 8 | 1 | no | — |
| 150 | C2×C4×C7 | — | 8 | 1 | no | — |
| 151 | C2×C4×C7 | #120 | 1 | 1 | yes | characteristic |
| 152 | C2×C4×C7 | AGL(1,ℤ/8) | 1 | 1 | yes | characteristic |
| 153 | C22⋊D7 | — | 8 | 2 | no | — |
| 154 | C22⋊D7 | — | 8 | 2 | no | — |
| 155 | C22⋊D7 | — | 8 | 1 | no | — |
| 156 | C22⋊D7 | — | 8 | 1 | no | — |
| 157 | C2×Dic7 | — | 2 | 1 | no | — |
| 158 | C2×Dic7 | — | 2 | 1 | no | — |
| 159 | C2×Dic7 | — | 2 | 1 | no | — |
| 160 | C2×Dic7 | — | 4 | 1 | no | — |
| 161 | C2×Dic7 | — | 4 | 2 | no | — |
| 162 | C2×Dic7 | — | 4 | 1 | no | — |
| 163 | C2×Dic7 | — | 8 | 2 | no | — |
| 164 | C2×Dic7 | — | 8 | 1 | no | — |
| 165 | C2×Dic7 | — | 8 | 1 | no | — |
| 166 | C2×Dic7 | SD32 | 1 | 2 | yes | complemented |
| 167 | D28 | — | 4 | 1 | no | — |
| 168 | D28 | — | 4 | 1 | no | — |
| 169 | C4×D7 | — | 8 | 2 | no | — |
| 170 | Dic14 | — | 4 | 2 | no | — |
| 171 | Dic14 | — | 4 | 2 | no | — |
| 172 | Dic14 | — | 8 | 2 | no | — |
| 173 | Dic14 | — | 8 | 1 | no | — |
| 174 | Dic14 | — | 8 | 1 | no | — |
| 175 | C7×C8 | — | 2 | 1 | no | — |
| 176 | C7×C8 | — | 2 | 1 | no | — |
| 177 | C7⋊C8 | — | 4 | 1 | no | — |
| 178 | C2×#41 | — | 28 | 1 | no | — |
| 179 | C22×Q8 | — | 14 | 1 | no | — |
| 180 | C2×Q16 | — | 14 | 1 | no | — |
| 181 | C2×Q16 | — | 14 | 1 | no | — |
| 182 | C2×Q16 | — | 28 | 2 | no | — |
| 183 | C2×D8 | — | 7 | 1 | no | — |
| 184 | C2×D8 | — | 14 | 1 | no | — |
| 185 | C2×D8 | D28 | 1 | 1 | yes | characteristic |
| 186 | C22×C8 | — | 7 | 1 | no | — |
| 187 | C22×C8 | C22×D7 | 1 | 1 | yes | characteristic |
| 188 | C4⋊Q8 | — | 14 | 1 | no | — |
| 189 | #127 | — | 14 | 1 | no | — |
| 190 | #124 | — | 28 | 1 | no | — |
| 191 | #121 | — | 2 | 1 | no | — |
| 192 | #121 | — | 14 | 1 | no | — |
| 193 | #121 | — | 28 | 1 | no | — |
| 194 | C4×D4 | — | 14 | 1 | no | — |
| 195 | C4×D4 | — | 14 | 1 | no | — |
| 196 | C4×D4 | — | 28 | 1 | no | — |
| 197 | C2×C4⋊C4 | — | 2 | 1 | no | — |
| 198 | C2×C42 | — | 7 | 1 | no | — |
| 199 | SD32 | — | 28 | 2 | no | — |
| 200 | SD32 | — | 28 | 2 | no | — |
| 201 | C2×C16 | — | 2 | 1 | no | — |
| 202 | C2×C16 | — | 14 | 1 | no | — |
| 203 | #107 | — | 7 | 1 | no | — |
| 204 | #107 | — | 14 | 1 | no | — |
| 205 | #107 | D28 | 1 | 1 | yes | characteristic |
| 206 | C4⋊C8 | — | 14 | 1 | no | — |
| 207 | C4⋊C8 | — | 14 | 1 | no | — |
| 208 | #103 | — | 28 | 2 | no | — |
| 209 | #102 | — | 2 | 1 | no | — |
| 210 | #102 | — | 14 | 1 | no | — |
| 211 | #102 | — | 14 | 1 | no | — |
| 212 | #102 | — | 14 | 1 | no | — |
| 213 | #95 | — | 28 | 1 | no | — |
| 214 | #95 | — | 28 | 1 | no | — |
| 215 | C22×C7 | — | 2 | 1 | no | — |
| 216 | C22×C7 | — | 2 | 1 | no | — |
| 217 | C22×C7 | — | 8 | 1 | no | — |
| 218 | C22×C7 | — | 8 | 1 | no | — |
| 219 | C22×C7 | — | 8 | 1 | no | — |
| 220 | C22×C7 | #447 | 1 | 1 | yes | characteristic |
| 221 | C22×C7 | C2×SD32 | 1 | 1 | yes | characteristic |
| 222 | C22×C7 | #509 | 1 | 1 | yes | characteristic |
| 223 | C2×D7 | — | 8 | 1 | no | — |
| 224 | C2×D7 | — | 8 | 1 | no | — |
| 225 | C2×D7 | — | 8 | 1 | no | — |
| 226 | C4×C7 | — | 2 | 1 | no | — |
| 227 | C4×C7 | — | 8 | 1 | no | — |
| 228 | C4×C7 | — | 16 | 1 | no | — |
| 229 | C4×C7 | #454 | 1 | 1 | yes | characteristic |
| 230 | C4×C7 | B(4,𝔽2) | 1 | 1 | yes | characteristic |
| 231 | Dic7 | — | 2 | 2 | no | — |
| 232 | Dic7 | — | 4 | 1 | no | — |
| 233 | Dic7 | — | 8 | 2 | no | — |
| 234 | Dic7 | — | 8 | 1 | no | — |
| 235 | #41 | — | 56 | 2 | no | — |
| 236 | #41 | — | 56 | 2 | no | — |
| 237 | C2×Q8 | — | 14 | 2 | no | — |
| 238 | C2×Q8 | — | 28 | 1 | no | — |
| 239 | C2×Q8 | — | 28 | 1 | no | — |
| 240 | C2×Q8 | — | 28 | 1 | no | — |
| 241 | C2×Q8 | — | 28 | 1 | no | — |
| 242 | C2×Q8 | — | 28 | 1 | no | — |
| 243 | C2×Q8 | — | 28 | 1 | no | — |
| 244 | C2×D4 | — | 2 | 1 | no | — |
| 245 | C2×D4 | — | 4 | 1 | no | — |
| 246 | C2×D4 | — | 14 | 1 | no | — |
| 247 | C2×D4 | — | 28 | 1 | no | — |
| 248 | C2×D4 | — | 28 | 1 | no | — |
| 249 | C2×D4 | — | 28 | 1 | no | — |
| 250 | C22×C4 | — | 4 | 1 | no | — |
| 251 | C22×C4 | — | 7 | 1 | no | — |
| 252 | C22×C4 | — | 7 | 1 | no | — |
| 253 | C22×C4 | — | 28 | 1 | no | — |
| 254 | C22×C4 | — | 28 | 1 | no | — |
| 255 | C22×C4 | — | 28 | 1 | no | — |
| 256 | C22×C4 | D4×D7 | 1 | 1 | yes | characteristic |
| 257 | Q16 | — | 14 | 2 | no | — |
| 258 | Q16 | — | 14 | 2 | no | — |
| 259 | Q16 | — | 28 | 1 | no | — |
| 260 | Q16 | — | 28 | 1 | no | — |
| 261 | D8 | — | 4 | 1 | no | — |
| 262 | D8 | — | 28 | 1 | no | — |
| 263 | D8 | — | 56 | 1 | no | — |
| 264 | C2×C8 | — | 4 | 1 | no | — |
| 265 | C2×C8 | — | 14 | 1 | no | — |
| 266 | C2×C8 | — | 28 | 1 | no | — |
| 267 | C2×C8 | C2×D28 | 1 | 1 | yes | characteristic |
| 268 | C2×C8 | D4×D7 | 1 | 1 | yes | characteristic |
| 269 | C4⋊C4 | — | 2 | 1 | no | — |
| 270 | C4⋊C4 | — | 4 | 1 | no | — |
| 271 | C4⋊C4 | — | 4 | 1 | no | — |
| 272 | C4⋊C4 | — | 14 | 1 | no | — |
| 273 | C4⋊C4 | — | 28 | 1 | no | — |
| 274 | C22⋊C4 | — | 4 | 1 | no | — |
| 275 | C22⋊C4 | — | 28 | 1 | no | — |
| 276 | C22⋊C4 | — | 28 | 1 | no | — |
| 277 | C22⋊C4 | — | 28 | 1 | no | — |
| 278 | C42 | — | 14 | 1 | no | — |
| 279 | C42 | — | 14 | 1 | no | — |
| 280 | C16 | — | 4 | 1 | no | — |
| 281 | C16 | — | 28 | 1 | no | — |
| 282 | C2×C7 | — | 2 | 1 | no | — |
| 283 | C2×C7 | — | 2 | 1 | no | — |
| 284 | C2×C7 | — | 16 | 1 | no | — |
| 285 | C2×C7 | #1598 | 1 | 1 | yes | characteristic |
| 286 | C2×C7 | #2187 | 1 | 1 | yes | characteristic |
| 287 | C2×C7 | #2191 | 1 | 1 | yes | characteristic |
| 288 | D7 | — | 16 | 1 | no | — |
| 289 | C23 | — | 4 | 1 | no | — |
| 290 | C23 | — | 28 | 1 | no | — |
| 291 | C23 | D7×D8 | 1 | 1 | yes | characteristic |
| 292 | Q8 | — | 28 | 2 | no | — |
| 293 | Q8 | — | 28 | 2 | no | — |
| 294 | Q8 | — | 56 | 1 | no | — |
| 295 | Q8 | — | 56 | 2 | no | — |
| 296 | Q8 | — | 56 | 1 | no | — |
| 297 | D4 | — | 4 | 1 | no | — |
| 298 | D4 | — | 4 | 1 | no | — |
| 299 | D4 | — | 8 | 1 | no | — |
| 300 | D4 | — | 8 | 1 | no | — |
| 301 | D4 | — | 28 | 1 | no | — |
| 302 | D4 | — | 28 | 1 | no | — |
| 303 | D4 | — | 56 | 2 | no | — |
| 304 | D4 | — | 56 | 2 | no | — |
| 305 | D4 | — | 56 | 1 | no | — |
| 306 | D4 | — | 56 | 1 | no | — |
| 307 | C2×C4 | — | 2 | 1 | no | — |
| 308 | C2×C4 | — | 2 | 1 | no | — |
| 309 | C2×C4 | — | 4 | 1 | no | — |
| 310 | C2×C4 | — | 7 | 2 | no | — |
| 311 | C2×C4 | — | 8 | 1 | no | — |
| 312 | C2×C4 | — | 8 | 1 | no | — |
| 313 | C2×C4 | — | 8 | 1 | no | — |
| 314 | C2×C4 | — | 14 | 1 | no | — |
| 315 | C2×C4 | — | 14 | 1 | no | — |
| 316 | C2×C4 | — | 14 | 1 | no | — |
| 317 | C2×C4 | — | 28 | 1 | no | — |
| 318 | C2×C4 | — | 28 | 2 | no | — |
| 319 | C2×C4 | — | 28 | 1 | no | — |
| 320 | C2×C4 | — | 56 | 2 | no | — |
| 321 | C2×C4 | — | 56 | 2 | no | — |
| 322 | C2×C4 | — | 56 | 1 | no | — |
| 323 | C2×C4 | — | 56 | 1 | no | — |
| 324 | C2×C4 | #6445 | 1 | 1 | yes | characteristic |
| 325 | C2×C4 | #6477 | 1 | 1 | yes | characteristic |
| 326 | C8 | — | 2 | 1 | no | — |
| 327 | C8 | — | 2 | 1 | no | — |
| 328 | C8 | — | 28 | 1 | no | — |
| 329 | C7 | #12161 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 330 | C22 | — | 2 | 1 | no | — |
| 331 | C22 | — | 2 | 1 | no | — |
| 332 | C22 | — | 8 | 1 | no | — |
| 333 | C22 | — | 8 | 1 | no | — |
| 334 | C22 | — | 8 | 1 | no | — |
| 335 | C22 | — | 56 | 1 | no | — |
| 336 | C22 | — | 56 | 1 | no | — |
| 337 | C22 | — | 56 | 1 | no | — |
| 338 | C22 | #89545 | 1 | 1 | yes | characteristic |
| 339 | C22 | #89683 | 1 | 1 | yes | characteristic |
| 340 | C22 | D7×SD32 | 1 | 1 | yes | characteristic |
| 341 | C4 | — | 2 | 1 | no | — |
| 342 | C4 | — | 8 | 1 | no | — |
| 343 | C4 | — | 14 | 2 | no | — |
| 344 | C4 | — | 16 | 1 | no | — |
| 345 | C4 | — | 28 | 1 | no | — |
| 346 | C4 | — | 56 | 1 | no | — |
| 347 | C4 | — | 56 | 2 | no | — |
| 348 | C4 | #89513 | 1 | 1 | yes | characteristic |
| 349 | C4 | #89599 | 1 | 1 | yes | characteristic |
| 350 | C2 | — | 2 | 1 | no | — |
| 351 | C2 | — | 2 | 1 | no | — |
| 352 | C2 | — | 16 | 1 | no | — |
| 353 | C2 | — | 112 | 1 | no | — |
| 354 | C2 | #11726047 | 1 | 1 | yes | characteristic |
| 355 | C2 | #11726947 | 1 | 1 | yes | characteristic |
| 356 | C2 | #11727007 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11728831 | C2 | semidirect |
| 3. #11726866 | C2 | semidirect |
| 4. #11726618 | C2 | semidirect |
| 5. C7×#1347 | C2 | semidirect |
| 6. #11725330 | C2 | semidirect |
| 7. #11725291 | C2 | semidirect |
| 70. #1347 | D7 | semidirect |
| 166. C2×Dic7 | SD32 | semidirect |
| 329. C7 | #12161 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11738147 | 2 |
| #11728831 | 2 |
| #11726866 | 2 |
| #11726618 | 2 |
| C7×#1347 | 2 |
| #11725330 | 2 |
| #11725291 | 2 |
| #12161 | 7 |