Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22578126 | C2 | semidirect |
| 2. #22578113 | C2 | semidirect |
| 3. #22577758 | C2 | semidirect |
| 4. #22577754 | C2 | semidirect |
| 5. #22577711 | C2 | semidirect |
| 6. #22577694 | C2 | semidirect |
| 8. #22577609 | C2 | semidirect |
| 9. C4×#14555499 | C2 | semidirect |
| 11. C8×Q8×C137 | C2 | semidirect |
| 120. C137 | #3360 | semidirect |
| 130. C8×Q8 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578126 | 2 |
| #22578113 | 2 |
| #22577758 | 2 |
| #22577754 | 2 |
| #22577711 | 2 |
| #22577694 | 2 |
| #22577619 | 2 |
| #22577609 | 2 |
| C4×#14555499 | 2 |
| C4×D1096 | 2 |
| C8×Q8×C137 | 2 |
| #3360 | 137 |