Finite Group DatabasebetaFinite Group DatabasebetaOrder 18176.
532 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22601474 | C2 | semidirect |
| 2. #22598002 | C2 | semidirect |
| 3. C2×#17985809 | C2 | semidirect |
| 4. #22590067 | C2 | semidirect |
| 5. #22589968 | C2 | semidirect |
| 6. #22586440 | C2 | semidirect |
| 7. C71×#3067 | C2 | semidirect |
| 56. C2×C71⋊C16 | D4 | semidirect |
| 72. C2×Q16×C71 | D4 | semidirect |
| 74. C2×D8×C71 | D4 | semidirect |
| 85. #108×C71 | D4 | semidirect |
| 228. #3067 | D71 | semidirect |
| 234. C71 | #13318 | semidirect |
| 277. C2×Q16 | C22⋊D71 | semidirect |
| 281. C2×D8 | C22⋊D71 | semidirect |
| 308. #108 | C22⋊D71 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22601474 | 2 |
| #22598002 | 2 |
| C2×#17985809 | 2 |
| #22590067 | 2 |
| #22589968 | 2 |
| #22586440 | 2 |
| C71×#3067 | 2 |
| #13318 | 71 |