Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
216 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 216 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. C2×#19151437 | C2 | semidirect |
| 3. #26022513 | C2 | semidirect |
| 4. C4×D1424 | C2 | semidirect |
| 5. #26018434 | C2 | semidirect |
| 6. #26018431 | C2 | semidirect |
| 7. C89×C4⋊C32 | C2 | semidirect |
| 102. C4⋊C32 | D89 | semidirect |
| 105. C89 | #13689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151437 | 2 |
| C2×D2848 | 2 |
| #26022513 | 2 |
| C4×D1424 | 2 |
| #26018434 | 2 |
| #26018431 | 2 |
| C89×C4⋊C32 | 2 |
| #13689 | 89 |