Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
560 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26029281 | C2 | semidirect |
| 3. #26018849 | C2 | semidirect |
| 4. #26018117 | C2 | semidirect |
| 5. C4×#100×C89 | C2 | semidirect |
| 43. #15667923 | D4 | semidirect |
| 203. C4×#100 | D89 | semidirect |
| 206. C89 | #9187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029281 | 2 |
| #26026104 | 2 |
| #26018849 | 2 |
| #26018117 | 2 |
| C4×#100×C89 | 2 |
| #9187 | 89 |