Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1152 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1152 conjugacy classes of subgroups — too many to draw. Only its 171 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. #26031239 | C2 | semidirect |
| 2. #26030716 | C2 | semidirect |
| 3. #26019558 | C2 | semidirect |
| 4. #26019541 | C2 | semidirect |
| 5. #26018876 | C2 | semidirect |
| 6. #26018850 | C2 | semidirect |
| 7. C2×H(3,𝔽4)×C89 | C2 | semidirect |
| 10. #19152148 | C22 | semidirect |
| 11. #19151993 | C22 | semidirect |
| 12. #19151988 | C22 | semidirect |
| 13. #19151988 | C22 | semidirect |
| 15. #19151957 | C22 | semidirect |
| 19. #19151655 | C22 | semidirect |
| 20. C4×#13083558 | C22 | semidirect |
| 21. #19151338 | C22 | semidirect |
| 22. #19151338 | C22 | semidirect |
| 42. #15668012 | C23 | semidirect |
| 43. #15668009 | C23 | semidirect |
| 51. #15667923 | C23 | semidirect |
| 52. #15667923 | C23 | semidirect |
| 207. C2×H(3,𝔽4) | D89 | semidirect |
| 214. C89 | #18992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031239 | 2 |
| #26030716 | 2 |
| #26019558 | 2 |
| #26019541 | 2 |
| #26018876 | 2 |
| #26018850 | 2 |
| C2×H(3,𝔽4)×C89 | 2 |
| #18992 | 89 |