Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
438 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 73 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. #26026449 | C2 | semidirect |
| 5. #26018137 | C2 | semidirect |
| 6. #26018106 | C2 | semidirect |
| 7. C89×#1305 | C2 | semidirect |
| 213. #1305 | D89 | semidirect |
| 216. C89 | #10384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26026449 | 2 |
| #26021087 | 2 |
| #26018782 | 2 |
| #26018769 | 2 |
| #26018137 | 2 |
| #26018106 | 2 |
| C89×#1305 | 2 |
| #10384 | 89 |