Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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×#17984111 | C2 | semidirect |
| 2. C2×#17984096 | C2 | semidirect |
| 3. #22577983 | C2 | semidirect |
| 4. #22577658 | C2 | semidirect |
| 5. #22577657 | C2 | semidirect |
| 6. #22577656 | C2 | semidirect |
| 7. #22577635 | C2 | semidirect |
| 8. #22577634 | C2 | semidirect |
| 9. #106×D137 | C2 | semidirect |
| 10. #22577403 | C2 | semidirect |
| 11. #470×C137 | C2 | semidirect |
| 65. C8×D137 | D4 | semidirect |
| 139. C137 | #3060 | semidirect |
| 145. #470 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984111 | 2 |
| C2×#17984096 | 2 |
| #22577983 | 2 |
| #22577658 | 2 |
| #22577657 | 2 |
| #22577656 | 2 |
| #22577635 | 2 |
| #22577634 | 2 |
| #106×D137 | 2 |
| #22577403 | 2 |
| #470×C137 | 2 |
| #3060 | 137 |