Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 103 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×#19152033 | C2 | semidirect |
| 2. C2×#19151975 | C2 | semidirect |
| 3. C2×#19151410 | C2 | semidirect |
| 4. #26018334 | C2 | semidirect |
| 5. C89×#1974 | C2 | semidirect |
| 37. #15667952 | D4 | semidirect |
| 42. C2×Q16×C89 | D4 | semidirect |
| 44. C2×D8×C89 | D4 | semidirect |
| 151. #1974 | D89 | semidirect |
| 153. C89 | #13331 | semidirect |
| 174. C2×Q16 | D356 | semidirect |
| 185. C2×D8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152033 | 2 |
| C2×#19151975 | 2 |
| C2×#19151410 | 2 |
| #26018334 | 2 |
| C89×#1974 | 2 |
| #13331 | 89 |