Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 402 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×C4×Q8×C89 | C4 | semidirect |
| 14. #400×C89 | C4 | semidirect |
| 18. #395×C89 | C4 | semidirect |
| 21. C4×C4⋊C4×C89 | C4 | semidirect |
| 170. C89 | #11810 | semidirect |
| 171. C2×C4×Q8 | Dic89 | semidirect |
| 174. #400 | Dic89 | semidirect |
| 178. #395 | Dic89 | semidirect |
| 182. C4×C4⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020329 | 2 |
| #26018586 | 2 |
| #26018276 | 2 |
| #26018273 | 2 |
| C89×#2396 | 2 |
| #11810 | 89 |