Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 10. #19152000 | C4 | semidirect |
| 11. #19151996 | C4 | semidirect |
| 49. M32×C89 | Q8 | semidirect |
| 51. C2×C16×C89 | Q8 | semidirect |
| 131. C89 | #13291 | semidirect |
| 162. M32 | Dic178 | semidirect |
| 164. C2×C16 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030783 | 2 |
| #26020376 | 2 |
| #26018367 | 2 |
| #26018358 | 2 |
| #26018354 | 2 |
| #26018351 | 2 |
| C89×#2110 | 2 |
| #13291 | 89 |