Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 105 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×#19152036 | C2 | semidirect |
| 2. C2×#19151975 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. #26021140 | C2 | semidirect |
| 5. C89×#1376 | C2 | semidirect |
| 26. C2×Dic356 | D4 | semidirect |
| 37. C2×D712 | D4 | semidirect |
| 50. M32×C89 | D4 | semidirect |
| 152. #1376 | D89 | semidirect |
| 153. C89 | #13331 | semidirect |
| 195. M32 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152036 | 2 |
| C2×#19151975 | 2 |
| C2×#19151412 | 2 |
| #26021140 | 2 |
| C89×#1376 | 2 |
| #13331 | 89 |