Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1770 conjugacy classes of subgroups; only the 451 normal subgroups are shown.
This group has 1770 conjugacy classes of subgroups — too many to draw. Only its 451 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 |
|---|---|---|
| 2. C2×#19151466 | C2 | semidirect |
| 4. #26018485 | C2 | semidirect |
| 5. C2×C43×C89 | C2 | semidirect |
| 8. C2×#15668006 | C4 | semidirect |
| 61. C42×C89 | C22⋊C4 | semidirect |
| 78. C2×C4×C89 | #126 | semidirect |
| 108. C2×C43 | D89 | semidirect |
| 111. C89 | #14711 | semidirect |
| 167. C42 | #13083551 | semidirect |
| 191. C2×C4 | #15668006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668006 | 2 |
| C2×#19151466 | 2 |
| #26018490 | 2 |
| #26018485 | 2 |
| C2×C43×C89 | 2 |
| #14711 | 89 |