Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
220 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 65 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. C4×Dic712 | C2 | semidirect |
| 4. #26018431 | C2 | semidirect |
| 5. C89×C4⋊C32 | C2 | semidirect |
| 22. Dic712 | D4 | semidirect |
| 70. C4×C89 | SD64 | semidirect |
| 83. C4⋊C32 | D89 | semidirect |
| 85. C89 | #13686 | semidirect |
| 152. C4 | #19151437 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151437 | 2 |
| #26022502 | 2 |
| C4×Dic712 | 2 |
| #26018431 | 2 |
| C89×C4⋊C32 | 2 |
| #13686 | 89 |