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. #22578138 | C2 | semidirect |
| 2. #22578110 | C2 | semidirect |
| 3. #22577759 | C2 | semidirect |
| 4. #22577750 | C2 | semidirect |
| 5. #22577702 | C2 | semidirect |
| 6. #22577698 | C2 | semidirect |
| 7. #22577620 | C2 | semidirect |
| 9. C8×Dic274 | C2 | semidirect |
| 10. #22577483 | C2 | semidirect |
| 11. C4×SD16×C137 | C2 | semidirect |
| 122. C137 | #3361 | semidirect |
| 133. C4×SD16 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578138 | 2 |
| #22578110 | 2 |
| #22577759 | 2 |
| #22577750 | 2 |
| #22577702 | 2 |
| #22577698 | 2 |
| #22577620 | 2 |
| #22577598 | 2 |
| C8×Dic274 | 2 |
| #22577483 | 2 |
| C4×SD16×C137 | 2 |
| #3361 | 137 |