Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
476 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 476 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 |
|---|---|---|
| 2. #26029170 | C2 | semidirect |
| 3. C2×#19151411 | C2 | semidirect |
| 4. #26021979 | C2 | semidirect |
| 5. #26018355 | C2 | semidirect |
| 6. #26018338 | C2 | semidirect |
| 7. C89×#1978 | C2 | semidirect |
| 12. C2×#15667956 | C4 | semidirect |
| 13. C2×#15667953 | C4 | semidirect |
| 175. #1978 | D89 | semidirect |
| 178. C89 | #13036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152034 | 2 |
| #26029170 | 2 |
| C2×#19151411 | 2 |
| #26021979 | 2 |
| #26018355 | 2 |
| #26018338 | 2 |
| C89×#1978 | 2 |
| #13036 | 89 |