Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. C2×#19151412 | C2 | semidirect |
| 3. #26021989 | C2 | semidirect |
| 4. #26021981 | C2 | semidirect |
| 5. #26021969 | C2 | semidirect |
| 6. #26020376 | C2 | semidirect |
| 7. C89×#2110 | C2 | semidirect |
| 13. #19151982 | C4 | semidirect |
| 14. #19151975 | C4 | semidirect |
| 62. M32×C89 | D4 | semidirect |
| 64. C2×C16×C89 | D4 | semidirect |
| 180. #2110 | D89 | semidirect |
| 182. C89 | #13215 | semidirect |
| 233. M32 | D356 | semidirect |
| 235. C2×C16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030738 | 2 |
| C2×#19151412 | 2 |
| #26021989 | 2 |
| #26021981 | 2 |
| #26021969 | 2 |
| #26020376 | 2 |
| C89×#2110 | 2 |
| #13215 | 89 |