Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#17984119 | C2 | semidirect |
| 2. C2×#17984095 | C2 | semidirect |
| 4. #22577659 | C2 | semidirect |
| 5. #22577651 | C2 | semidirect |
| 6. #22577642 | C2 | semidirect |
| 7. #22577634 | C2 | semidirect |
| 8. #22577446 | C2 | semidirect |
| 9. #22577397 | C2 | semidirect |
| 10. C2×#17984012 | C2 | semidirect |
| 11. #536×C137 | C2 | semidirect |
| 54. #14555494 | D4 | semidirect |
| 143. C137 | #3063 | semidirect |
| 148. #536 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984119 | 2 |
| C2×#17984095 | 2 |
| #22577981 | 2 |
| #22577659 | 2 |
| #22577651 | 2 |
| #22577642 | 2 |
| #22577634 | 2 |
| #22577446 | 2 |
| #22577397 | 2 |
| C2×#17984012 | 2 |
| #536×C137 | 2 |
| #3063 | 137 |