Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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×#19151721 | C2 | semidirect |
| 3. #26021999 | C2 | semidirect |
| 4. #26021980 | C2 | semidirect |
| 5. #26018365 | C2 | semidirect |
| 6. #26018336 | C2 | semidirect |
| 7. C89×#1975 | C2 | semidirect |
| 10. #19152039 | C4 | semidirect |
| 12. #19152034 | C4 | semidirect |
| 186. #1975 | D89 | semidirect |
| 189. C89 | #13024 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| C2×#19151721 | 2 |
| #26021999 | 2 |
| #26021980 | 2 |
| #26018365 | 2 |
| #26018336 | 2 |
| C89×#1975 | 2 |
| #13024 | 89 |