Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26030784 | C2 | semidirect |
| 4. #26018358 | C2 | semidirect |
| 5. #26018353 | C2 | semidirect |
| 6. #26018337 | C2 | semidirect |
| 52. C2×Q16×C89 | Q8 | semidirect |
| 54. C2×D8×C89 | Q8 | semidirect |
| 164. C89 | #13374 | semidirect |
| 187. C2×Q16 | Dic178 | semidirect |
| 189. C2×D8 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030784 | 2 |
| C2×#19151408 | 2 |
| #26021151 | 2 |
| #26018358 | 2 |
| #26018353 | 2 |
| #26018337 | 2 |
| C89×#2145 | 2 |
| #13374 | 89 |