Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
564 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#19151342 | C2 | semidirect |
| 3. #26018396 | C2 | direct (N × H) |
| 4. C2×#353×C89 | C2 | semidirect |
| 5. C2×#15668057 | C4 | semidirect |
| 9. #19151765 | C4 | semidirect |
| 13. C2×#15667929 | C4 | semidirect |
| 15. #19151342 | C22 | semidirect |
| 19. #353×C89 | C22 | semidirect |
| 23. #15668057 | C2×C4 | semidirect |
| 40. #15667929 | C2×C4 | semidirect |
| 195. C2×C89 | #1402 | semidirect |
| 199. C2×#353 | D89 | semidirect |
| 202. C89 | C2×#1402 | semidirect |
| 215. #353 | C2×D89 | semidirect |
| 393. C2 | #26018396 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151765 | 2 |
| C2×#19151342 | 2 |
| #26018396 | 2 |
| C2×#353×C89 | 2 |
| C2×#1402 | 89 |