Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 4. #22560424 | C2 | semidirect |
| 5. #22558336 | C2 | semidirect |
| 6. #22558335 | C2 | semidirect |
| 7. C67×#1857 | C2 | semidirect |
| 20. #16863192 | C4 | semidirect |
| 53. #14523962 | C2×C4 | semidirect |
| 70. #101×C67 | C2×C4 | semidirect |
| 212. #1857 | D67 | semidirect |
| 215. C67 | #12972 | semidirect |
| 274. #101 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22563320 | 2 |
| C2×#16863192 | 2 |
| #22560612 | 2 |
| #22560424 | 2 |
| #22558336 | 2 |
| #22558335 | 2 |
| C67×#1857 | 2 |
| #12972 | 67 |