Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
204 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19151431 | C2 | semidirect |
| 2. C2×C32×D89 | C2 | semidirect |
| 4. #26018389 | C2 | semidirect |
| 5. #26018389 | C2 | semidirect |
| 6. #26018386 | C2 | semidirect |
| 7. C89×C4⋊C32 | C2 | semidirect |
| 34. #15667918 | D4 | semidirect |
| 83. C2×D89 | M64 | semidirect |
| 99. C4⋊C32 | D89 | semidirect |
| 103. C89 | #13645 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151431 | 2 |
| C2×C32×D89 | 2 |
| C16×D356 | 2 |
| #26018389 | 2 |
| #26018386 | 2 |
| C89×C4⋊C32 | 2 |
| #13645 | 89 |