Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
512 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 111 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. #26022726 | C2 | semidirect |
| 5. #26018680 | C2 | semidirect |
| 6. #26018084 | C2 | semidirect |
| 7. C89×#1303 | C2 | semidirect |
| 11. #19151884 | C4 | semidirect |
| 12. #19151799 | C4 | semidirect |
| 107. C4×Dic89 | SD16 | semidirect |
| 201. #1303 | D89 | semidirect |
| 203. C89 | #9238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030284 | 2 |
| #26022726 | 2 |
| #26021079 | 2 |
| #26018746 | 2 |
| #26018680 | 2 |
| #26018084 | 2 |
| C89×#1303 | 2 |
| #9238 | 89 |