Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22578139 | C2 | semidirect |
| 2. #22578110 | C2 | semidirect |
| 3. #22577756 | C2 | semidirect |
| 4. #22577749 | C2 | semidirect |
| 5. #22577701 | C2 | semidirect |
| 6. #22577699 | C2 | semidirect |
| 7. #22577616 | C2 | semidirect |
| 8. #22577527 | C2 | semidirect |
| 9. C4×#14555498 | C2 | semidirect |
| 10. D8×Dic137 | C2 | semidirect |
| 122. C137 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578139 | 2 |
| #22578110 | 2 |
| #22577756 | 2 |
| #22577749 | 2 |
| #22577701 | 2 |
| #22577699 | 2 |
| #22577616 | 2 |
| #22577527 | 2 |
| C4×#14555498 | 2 |
| D8×Dic137 | 2 |
| #459×C137 | 2 |
| #3361 | 137 |