Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1082 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22574614 | C2 | semidirect |
| 2. #22571587 | C2 | semidirect |
| 3. #22559352 | C2 | semidirect |
| 4. #22559323 | C2 | semidirect |
| 5. #22559290 | C2 | semidirect |
| 6. #22559261 | C2 | semidirect |
| 7. #22558944 | C2 | semidirect |
| 8. #22558661 | C2 | semidirect |
| 9. C67×#3147 | C2 | semidirect |
| 19. #16863683 | C22 | semidirect |
| 22. #16863588 | C22 | semidirect |
| 23. #16863420 | C22 | semidirect |
| 24. #16863145 | C22 | semidirect |
| 26. #16863125 | C22 | semidirect |
| 27. #16863125 | C22 | semidirect |
| 30. #532×C67 | C22 | semidirect |
| 32. #494×C67 | C22 | semidirect |
| 35. #492×C67 | C22 | semidirect |
| 36. C2×C4×C8×C67 | C22 | semidirect |
| 208. #3147 | D67 | semidirect |
| 215. C67 | #18686 | semidirect |
| 226. #532 | C2×D67 | semidirect |
| 228. #494 | C2×D67 | semidirect |
| 231. #492 | C2×D67 | semidirect |
| 238. C2×C4×C8 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574614 | 2 |
| #22571587 | 2 |
| #22559352 | 2 |
| #22559323 | 2 |
| #22559290 | 2 |
| #22559261 | 2 |
| #22558944 | 2 |
| #22558661 | 2 |
| C67×#3147 | 2 |
| #18686 | 67 |