Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
432 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26020329 | C2 | semidirect |
| 2. #26018566 | C2 | semidirect |
| 3. #26018273 | C2 | semidirect |
| 12. C2×#124×C89 | C4 | semidirect |
| 14. #395×C89 | C4 | semidirect |
| 15. #394×C89 | C4 | semidirect |
| 22. #376×C89 | C4 | semidirect |
| 186. C89 | #11844 | semidirect |
| 187. C2×#124 | Dic89 | semidirect |
| 190. #395 | Dic89 | semidirect |
| 191. #394 | Dic89 | semidirect |
| 199. #376 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020329 | 2 |
| #26018566 | 2 |
| #26018273 | 2 |
| #26018249 | 2 |
| C89×#2610 | 2 |
| #11844 | 89 |