Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
388 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26022046 | C2 | semidirect |
| 5. #26018368 | C2 | semidirect |
| 6. #26018336 | C2 | semidirect |
| 7. C89×#1946 | C2 | semidirect |
| 17. #19151407 | C4 | semidirect |
| 148. #1946 | D89 | semidirect |
| 151. C89 | #12944 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151721 | 2 |
| #26022046 | 2 |
| #26021987 | 2 |
| #26021979 | 2 |
| #26018368 | 2 |
| #26018336 | 2 |
| C89×#1946 | 2 |
| #12944 | 89 |