Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
170 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26022531 | C2 | semidirect |
| 3. #26018454 | C2 | semidirect |
| 4. #26018452 | C2 | semidirect |
| 7. C89×C4⋊C32 | C2 | semidirect |
| 83. C4⋊C32 | D89 | semidirect |
| 86. C89 | #13707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022531 | 2 |
| C4×D1424 | 2 |
| #26018454 | 2 |
| #26018452 | 2 |
| #26018431 | 2 |
| C89×C4⋊C32 | 2 |
| #13707 | 89 |