Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 4. C2×#19151375 | C2 | semidirect |
| 5. #26020139 | C2 | semidirect |
| 6. #26018353 | C2 | semidirect |
| 7. C89×#1389 | C2 | semidirect |
| 11. #19151709 | C4 | semidirect |
| 12. #19151704 | C4 | semidirect |
| 18. #19151409 | C4 | semidirect |
| 19. #19151404 | C4 | semidirect |
| 43. C2×#13083549 | C2×C4 | semidirect |
| 45. #15667944 | C2×C4 | semidirect |
| 56. M32×C89 | C2×C4 | semidirect |
| 59. #108×C89 | C2×C4 | semidirect |
| 157. #1389 | D89 | semidirect |
| 159. C89 | #12649 | semidirect |
| 199. M32 | C4×D89 | semidirect |
| 203. #108 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029052 | 2 |
| #26021989 | 2 |
| #26021979 | 2 |
| C2×#19151375 | 2 |
| #26020139 | 2 |
| #26018353 | 2 |
| C89×#1389 | 2 |
| #12649 | 89 |