Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
716 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. C2×#19151529 | C2 | semidirect |
| 5. C2×#19151323 | C2 | semidirect |
| 6. #26018130 | C2 | semidirect |
| 7. C89×#1823 | C2 | semidirect |
| 252. #1823 | D89 | semidirect |
| 256. C89 | #9919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151911 | 2 |
| #26025997 | 2 |
| C2×#19151529 | 2 |
| C2×#19151333 | 2 |
| C2×#19151323 | 2 |
| #26018130 | 2 |
| C89×#1823 | 2 |
| #9919 | 89 |