Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1006 conjugacy classes of subgroups; only the 255 normal subgroups are shown.
This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 255 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×#19151719 | C2 | semidirect |
| 3. #26028963 | C2 | semidirect |
| 4. #26021138 | C2 | semidirect |
| 5. #26021083 | C2 | semidirect |
| 6. #26019940 | C2 | semidirect |
| 7. C89×#1849 | C2 | semidirect |
| 11. #19151992 | C4 | semidirect |
| 12. #19151987 | C4 | semidirect |
| 44. #15667922 | D4 | semidirect |
| 126. #1849 | D89 | semidirect |
| 128. C89 | #21709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030698 | 2 |
| C2×#19151719 | 2 |
| #26028963 | 2 |
| #26021138 | 2 |
| #26021083 | 2 |
| #26019940 | 2 |
| C89×#1849 | 2 |
| #21709 | 89 |