Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
602 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 105 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. #22569249 | C2 | semidirect |
| 3. #22560198 | C2 | semidirect |
| 4. #22558635 | C2 | semidirect |
| 5. #22558633 | C2 | semidirect |
| 6. #22558067 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 56. C4×C67⋊C8 | D4 | semidirect |
| 65. C4×C8×C67 | D4 | semidirect |
| 216. #1286 | D67 | semidirect |
| 217. C67 | #9489 | semidirect |
| 274. C4×C8 | D268 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569249 | 2 |
| #22565111 | 2 |
| #22560198 | 2 |
| #22558635 | 2 |
| #22558633 | 2 |
| #22558067 | 2 |
| C67×#1286 | 2 |
| #9489 | 67 |