Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
420 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 71 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×#19151393 | C2 | semidirect |
| 3. #26018413 | C2 | semidirect |
| 4. #26018410 | C2 | semidirect |
| 5. C2×#355×C89 | C2 | semidirect |
| 8. #19152148 | C4 | semidirect |
| 9. #19151993 | C4 | semidirect |
| 11. #19151988 | C4 | semidirect |
| 16. C4×#13083558 | C4 | semidirect |
| 37. #15668012 | C2×C4 | semidirect |
| 38. #15668009 | C2×C4 | semidirect |
| 45. #15667923 | C2×C4 | semidirect |
| 46. #15667923 | C2×C4 | semidirect |
| 178. C2×#355 | D89 | semidirect |
| 182. C89 | #13578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030716 | 2 |
| C2×#19151393 | 2 |
| #26018413 | 2 |
| #26018410 | 2 |
| C2×#355×C89 | 2 |
| #13578 | 89 |