Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
126 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 43 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. #22577800 | C2 | semidirect |
| 3. #22577227 | C2 | semidirect |
| 4. #22577223 | C2 | semidirect |
| 7. #365×C137 | C2 | semidirect |
| 21. Dic548 | Q8 | semidirect |
| 23. D1096 | Q8 | semidirect |
| 60. C137 | #2230 | semidirect |
| 65. #365 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577800 | 2 |
| #22577519 | 2 |
| #22577227 | 2 |
| #22577223 | 2 |
| #22577214 | 2 |
| #22577212 | 2 |
| #365×C137 | 2 |
| #2230 | 137 |