Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
388 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #26021003 | C2 | semidirect |
| 5. #26018366 | C2 | semidirect |
| 6. #26018335 | C2 | semidirect |
| 7. C89×#2161 | C2 | semidirect |
| 17. #19151409 | C4 | semidirect |
| 145. #2161 | 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×#19151719 | 2 |
| #26021989 | 2 |
| #26021979 | 2 |
| #26021003 | 2 |
| #26018366 | 2 |
| #26018335 | 2 |
| C89×#2161 | 2 |
| #12944 | 89 |