Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 59 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. #355×D89 | C2 | semidirect |
| 3. #354×D89 | C2 | semidirect |
| 4. #26018413 | C2 | semidirect |
| 5. #26018411 | C2 | semidirect |
| 6. #26018409 | C2 | semidirect |
| 7. C89×#1406 | C2 | semidirect |
| 10. #19152146 | C4 | semidirect |
| 13. #19151992 | C4 | semidirect |
| 14. #19151985 | C4 | semidirect |
| 19. #19151550 | C4 | semidirect |
| 42. #15668012 | C2×C4 | semidirect |
| 57. #15667923 | C2×C4 | semidirect |
| 61. #127×C89 | C2×C4 | semidirect |
| 65. #97×C89 | C2×C4 | semidirect |
| 194. #1406 | D89 | semidirect |
| 195. C89 | #13578 | semidirect |
| 233. #127 | C4×D89 | semidirect |
| 252. #97 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030717 | 2 |
| #355×D89 | 2 |
| #354×D89 | 2 |
| #26018413 | 2 |
| #26018411 | 2 |
| #26018409 | 2 |
| C89×#1406 | 2 |
| #13578 | 89 |