Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
252 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22562466 | C2 | semidirect |
| 2. #22562028 | C2 | semidirect |
| 3. #22559571 | C2 | semidirect |
| 5. #22558282 | C2 | semidirect |
| 6. #22558256 | C2 | semidirect |
| 7. C67×#1362 | C2 | semidirect |
| 62. C67⋊C16 | D8 | semidirect |
| 89. D268 | SD32 | semidirect |
| 123. #1362 | D67 | semidirect |
| 125. C67 | #12432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562466 | 2 |
| #22562028 | 2 |
| #22559571 | 2 |
| #22559565 | 2 |
| #22558282 | 2 |
| #22558256 | 2 |
| C67×#1362 | 2 |
| #12432 | 67 |