Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
572 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 139 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. C2×#19151407 | C2 | semidirect |
| 3. #26021863 | C2 | semidirect |
| 4. #26018359 | C2 | semidirect |
| 5. C22×#106×C89 | C2 | semidirect |
| 9. #19151839 | C4 | semidirect |
| 10. #19151834 | C4 | semidirect |
| 24. C2×Dic356 | C2×C4 | semidirect |
| 26. C2×D712 | C2×C4 | semidirect |
| 36. #15667946 | C2×C4 | semidirect |
| 54. #106×C89 | D4 | semidirect |
| 139. C22×C89 | #360 | semidirect |
| 161. C22×#106 | D89 | semidirect |
| 165. C89 | #13001 | semidirect |
| 212. #106 | C22⋊D89 | semidirect |
| 301. C22 | #19151407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029833 | 2 |
| C2×#19151407 | 2 |
| #26021863 | 2 |
| #26018359 | 2 |
| C22×#106×C89 | 2 |
| #13001 | 89 |