Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1026 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 1026 conjugacy classes of subgroups — too many to draw. Only its 151 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. #26018377 | C2 | semidirect |
| 4. #26018376 | C2 | semidirect |
| 5. C89×#1393 | C2 | semidirect |
| 7. C2×#15667970 | C4 | semidirect |
| 8. C2×#15667969 | C4 | semidirect |
| 13. #99×D89 | C4 | semidirect |
| 15. #19151500 | C4 | semidirect |
| 16. #19151499 | C4 | semidirect |
| 33. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 45. C2×C4×Dic89 | C2×C4 | semidirect |
| 47. #15667927 | C2×C4 | semidirect |
| 50. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 53. C2×C42×C89 | C2×C4 | semidirect |
| 55. #99×C89 | C2×C4 | semidirect |
| 225. #1393 | D89 | semidirect |
| 226. C89 | #12582 | semidirect |
| 257. C2×C4⋊C4 | C4×D89 | semidirect |
| 271. C2×C42 | C4×D89 | semidirect |
| 276. #99 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#99×D89 | 2 |
| #26022831 | 2 |
| #26018377 | 2 |
| #26018376 | 2 |
| C89×#1393 | 2 |
| #12582 | 89 |