Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
586 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 586 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 3. #26018277 | C2 | semidirect |
| 4. #26018253 | C2 | semidirect |
| 6. C2×#15667971 | C4 | semidirect |
| 8. #19151534 | C4 | semidirect |
| 10. #19151523 | C4 | semidirect |
| 15. #19151461 | C4 | semidirect |
| 26. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 27. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 44. #15667919 | C2×C4 | semidirect |
| 45. #15667919 | C2×C4 | semidirect |
| 220. C89 | #11755 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024526 | 2 |
| C2×#19151365 | 2 |
| #26018277 | 2 |
| #26018253 | 2 |
| C89×#1462 | 2 |
| #11755 | 89 |