Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 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. #22578123 | C2 | semidirect |
| 2. #22578110 | C2 | semidirect |
| 3. #22577756 | C2 | semidirect |
| 4. #22577754 | C2 | semidirect |
| 5. #22577709 | C2 | semidirect |
| 6. #22577693 | C2 | semidirect |
| 8. #22577608 | C2 | semidirect |
| 9. C8×Dic274 | C2 | semidirect |
| 10. #22577494 | C2 | semidirect |
| 120. C137 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578123 | 2 |
| #22578110 | 2 |
| #22577756 | 2 |
| #22577754 | 2 |
| #22577709 | 2 |
| #22577693 | 2 |
| #22577616 | 2 |
| #22577608 | 2 |
| C8×Dic274 | 2 |
| #22577494 | 2 |
| C4×D8×C137 | 2 |
| #3360 | 137 |