Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
484 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#17984121 | C2 | semidirect |
| 2. C2×#17984118 | C2 | semidirect |
| 4. C2×#17984053 | C2 | semidirect |
| 5. #22577628 | C2 | semidirect |
| 6. #22577624 | C2 | semidirect |
| 7. #22577612 | C2 | semidirect |
| 8. #22577602 | C2 | semidirect |
| 9. #22577426 | C2 | semidirect |
| 10. #22577402 | C2 | semidirect |
| 11. #417×C137 | C2 | semidirect |
| 49. C2×Dic274 | D4 | semidirect |
| 150. Dic137 | #137 | semidirect |
| 157. C137 | #3037 | semidirect |
| 169. #417 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984121 | 2 |
| C2×#17984118 | 2 |
| #22577949 | 2 |
| C2×#17984053 | 2 |
| #22577628 | 2 |
| #22577624 | 2 |
| #22577612 | 2 |
| #22577602 | 2 |
| #22577426 | 2 |
| #22577402 | 2 |
| #417×C137 | 2 |
| #3037 | 137 |