Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
| 20. #384×C89 | C4 | semidirect |
| 21. #382×C89 | C4 | semidirect |
| 22. C4×C4⋊C4×C89 | C4 | semidirect |
| 198. C89 | #13300 | semidirect |
| 199. C2×#125 | Dic89 | semidirect |
| 209. #384 | Dic89 | semidirect |
| 210. #382 | Dic89 | semidirect |
| 212. C4×C4⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020240 | 2 |
| C4×#15667927 | 2 |
| #26018377 | 2 |
| C89×#2566 | 2 |
| #13300 | 89 |