Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
602 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26025917 | C2 | semidirect |
| 3. #26018160 | C2 | semidirect |
| 4. #26018104 | C2 | semidirect |
| 38. C22×Q8×C89 | Q8 | semidirect |
| 40. C22×D4×C89 | Q8 | semidirect |
| 176. C89 | #10386 | semidirect |
| 195. C22×Q8 | Dic178 | semidirect |
| 197. C22×D4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025917 | 2 |
| #26020196 | 2 |
| #26018160 | 2 |
| #26018104 | 2 |
| C89×#1782 | 2 |
| #10386 | 89 |