Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
396 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 191 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. Q8×#11764049 | C2 | semidirect |
| 18. C2×Dic274 | C8 | semidirect |
| 19. Q8×D137 | C8 | semidirect |
| 22. C2×Q8×C137 | C8 | semidirect |
| 51. C137 | #2982 | semidirect |
| 67. C2×Q8 | #11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11764049 | 2 |
| #22578516 | 2 |
| C2×Q8×#10587739 | 2 |
| #2982 | 137 |