Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1150 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1150 conjugacy classes of subgroups — too many to draw. Only its 187 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 |
|---|---|---|
| 1. C2×#19151993 | C2 | semidirect |
| 2. C2×#19151957 | C2 | semidirect |
| 3. #26019558 | C2 | direct (N × H) |
| 4. C2×#19151338 | C2 | semidirect |
| 5. C2×#19151338 | C2 | semidirect |
| 9. C2×#15668012 | C22 | semidirect |
| 11. #19151993 | C22 | semidirect |
| 13. #19151957 | C22 | semidirect |
| 16. C2×#15667923 | C22 | semidirect |
| 17. C2×#15667923 | C22 | semidirect |
| 18. #19151338 | C22 | semidirect |
| 19. #19151338 | C22 | semidirect |
| 38. #15668012 | C23 | semidirect |
| 44. #15667923 | C23 | semidirect |
| 45. #15667923 | C23 | semidirect |
| 184. C2×C89 | #1659 | semidirect |
| 193. C89 | C2×#1659 | semidirect |
| 370. C2 | #26019558 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151993 | 2 |
| C2×#19151957 | 2 |
| #26019558 | 2 |
| C2×#19151338 | 2 |
| C2×H(3,𝔽4)×C89 | 2 |
| C2×#1659 | 89 |