Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
406 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 406 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. #26020998 | C2 | semidirect |
| 5. #26018353 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 7. C89×#2155 | C2 | semidirect |
| 20. #19151409 | C4 | semidirect |
| 46. #15667944 | C2×C4 | semidirect |
| 56. M32×C89 | C2×C4 | semidirect |
| 156. #2155 | D89 | semidirect |
| 162. C89 | #12951 | semidirect |
| 203. M32 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029023 | 2 |
| #26021999 | 2 |
| #26021989 | 2 |
| #26020998 | 2 |
| #26018353 | 2 |
| #26018333 | 2 |
| C89×#2155 | 2 |
| #12951 | 89 |