Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
778 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 778 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 |
|---|---|---|
| 2. #26018579 | C2 | semidirect |
| 3. #26018272 | C2 | semidirect |
| 4. #26018248 | C2 | semidirect |
| 5. C2×#342×C89 | C2 | semidirect |
| 6. C22×#13083574 | C4 | semidirect |
| 9. #19151510 | C4 | semidirect |
| 11. #19151507 | C4 | semidirect |
| 16. #19151461 | C4 | semidirect |
| 26. C22×Dic178 | C2×C4 | semidirect |
| 27. C22×D356 | C2×C4 | semidirect |
| 44. #15667919 | C2×C4 | semidirect |
| 45. #15667919 | C2×C4 | semidirect |
| 253. C2×#342 | D89 | semidirect |
| 257. C89 | #11753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023571 | 2 |
| #26018579 | 2 |
| #26018272 | 2 |
| #26018248 | 2 |
| C2×#342×C89 | 2 |
| #11753 | 89 |