Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 51. C22×Q8×C89 | Q8 | semidirect |
| 60. C2×C4⋊C4×C89 | Q8 | semidirect |
| 218. C89 | #10375 | semidirect |
| 239. C22×Q8 | Dic178 | semidirect |
| 258. C2×C4⋊C4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025263 | 2 |
| #26021238 | 2 |
| #26018824 | 2 |
| #26018131 | 2 |
| #26018120 | 2 |
| #26018098 | 2 |
| C2×#328×C89 | 2 |
| #10375 | 89 |