Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
416 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26018413 | C2 | semidirect |
| 5. #26018412 | C2 | semidirect |
| 6. #26018411 | C2 | semidirect |
| 7. C89×#1407 | C2 | semidirect |
| 10. C4⋊Q8×D89 | C4 | semidirect |
| 13. #19151992 | C4 | semidirect |
| 15. #19151990 | C4 | semidirect |
| 19. #97×D89 | C4 | semidirect |
| 42. #15668012 | C2×C4 | semidirect |
| 57. #15667923 | C2×C4 | semidirect |
| 61. C4⋊Q8×C89 | C2×C4 | semidirect |
| 65. #97×C89 | C2×C4 | semidirect |
| 184. D89 | #1407 | direct (N × H) |
| 191. #1407 | D89 | direct (N × H) |
| 192. C89 | C2×#1407 | semidirect |
| 232. C4⋊Q8 | C4×D89 | semidirect |
| 250. #97 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #497×D89 | 2 |
| #355×D89 | 2 |
| #354×D89 | 2 |
| #26018413 | 2 |
| #26018412 | 2 |
| #26018411 | 2 |
| C89×#1407 | 2 |
| C2×#1407 | 89 |