Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26029105 | C2 | semidirect |
| 3. C2×#19151410 | C2 | semidirect |
| 4. #26021968 | C2 | semidirect |
| 5. #26018349 | C2 | semidirect |
| 6. #26018341 | C2 | semidirect |
| 7. C89×#1978 | C2 | semidirect |
| 12. C2×#15667953 | C4 | semidirect |
| 43. C2×#13083549 | C2×C4 | semidirect |
| 53. C2×D8×C89 | C2×C4 | semidirect |
| 170. #1978 | D89 | semidirect |
| 173. C89 | #13017 | semidirect |
| 205. C2×D8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667953 | 2 |
| #26029105 | 2 |
| C2×#19151410 | 2 |
| #26021968 | 2 |
| #26018349 | 2 |
| #26018341 | 2 |
| C89×#1978 | 2 |
| #13017 | 89 |