Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
378 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 378 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 |
|---|---|---|
| 1. #26030792 | C2 | semidirect |
| 4. #26018361 | C2 | semidirect |
| 5. #26018347 | C2 | semidirect |
| 6. #26018342 | C2 | semidirect |
| 54. C2×D8×C89 | Q8 | semidirect |
| 166. C89 | #13369 | semidirect |
| 190. C2×D8 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030792 | 2 |
| C2×#19151399 | 2 |
| #26021163 | 2 |
| #26018361 | 2 |
| #26018347 | 2 |
| #26018342 | 2 |
| C89×#2140 | 2 |
| #13369 | 89 |