Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
668 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 147 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×#19152040 | C2 | semidirect |
| 2. #26031994 | C2 | semidirect |
| 3. #26022513 | C2 | semidirect |
| 4. #26022366 | C2 | semidirect |
| 5. #26022314 | C2 | semidirect |
| 6. #26022187 | C2 | semidirect |
| 7. #26022178 | C2 | semidirect |
| 8. #26022085 | C2 | semidirect |
| 9. C4×Q32×C89 | C2 | semidirect |
| 69. Q32×C89 | D4 | semidirect |
| 172. C4×Q32 | D89 | semidirect |
| 174. C89 | #33843 | semidirect |
| 225. Q32 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152040 | 2 |
| #26031994 | 2 |
| #26022513 | 2 |
| #26022366 | 2 |
| #26022314 | 2 |
| #26022187 | 2 |
| #26022178 | 2 |
| #26022085 | 2 |
| C4×Q32×C89 | 2 |
| #33843 | 89 |