Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26020467 | C2 | semidirect |
| 5. #26018379 | C2 | semidirect |
| 6. #26018378 | C2 | semidirect |
| 7. C89×#1857 | C2 | semidirect |
| 20. #19151394 | C4 | semidirect |
| 53. #15667931 | C2×C4 | semidirect |
| 70. #101×C89 | C2×C4 | semidirect |
| 212. #1857 | D89 | semidirect |
| 215. C89 | #12972 | semidirect |
| 274. #101 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023363 | 2 |
| C2×#19151394 | 2 |
| #26020655 | 2 |
| #26020467 | 2 |
| #26018379 | 2 |
| #26018378 | 2 |
| C89×#1857 | 2 |
| #12972 | 89 |