Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
382 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 12. C2×#125×C89 | C4 | semidirect |
| 14. #400×C89 | C4 | semidirect |
| 16. #398×C89 | C4 | semidirect |
| 22. #376×C89 | C4 | semidirect |
| 166. C89 | #11846 | semidirect |
| 167. C2×#125 | Dic89 | semidirect |
| 170. #400 | Dic89 | semidirect |
| 172. #398 | Dic89 | semidirect |
| 179. #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 |
| #26018276 | 2 |
| #26018252 | 2 |
| C89×#2611 | 2 |
| #11846 | 89 |