Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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×#19151425 | C2 | semidirect |
| 5. #26018362 | C2 | semidirect |
| 6. #26018341 | C2 | semidirect |
| 7. C89×#1952 | C2 | semidirect |
| 18. #19151404 | C4 | semidirect |
| 45. C2×#13083549 | C2×C4 | semidirect |
| 56. #108×C89 | C2×C4 | semidirect |
| 164. #1952 | D89 | semidirect |
| 167. C89 | #12946 | semidirect |
| 212. #108 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029129 | 2 |
| C2×#19151425 | 2 |
| C2×#19151404 | 2 |
| #26021962 | 2 |
| #26018362 | 2 |
| #26018341 | 2 |
| C89×#1952 | 2 |
| #12946 | 89 |