Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
568 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 101 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. #26033388 | C2 | semidirect |
| 2. C2×#19152036 | C2 | semidirect |
| 3. #26030738 | C2 | semidirect |
| 4. #26021989 | C2 | semidirect |
| 5. #26021969 | C2 | semidirect |
| 6. #26021150 | C2 | semidirect |
| 7. C89×#1378 | C2 | semidirect |
| 47. C2×Dic356 | D4 | semidirect |
| 59. C2×D712 | D4 | semidirect |
| 81. M32×C89 | D4 | semidirect |
| 83. C2×C16×C89 | D4 | semidirect |
| 224. #1378 | D89 | semidirect |
| 225. C89 | #13334 | semidirect |
| 295. M32 | D356 | semidirect |
| 297. C2×C16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033388 | 2 |
| C2×#19152036 | 2 |
| #26030738 | 2 |
| #26021989 | 2 |
| #26021969 | 2 |
| #26021150 | 2 |
| C89×#1378 | 2 |
| #13334 | 89 |