Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1064 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 187 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. #26031027 | C2 | semidirect |
| 4. #26019279 | C2 | semidirect |
| 5. #26019211 | C2 | semidirect |
| 6. #26018825 | C2 | semidirect |
| 18. #19151934 | C22 | semidirect |
| 21. #19151756 | C22 | semidirect |
| 28. #19151336 | C22 | semidirect |
| 121. C24×C89 | Q16 | semidirect |
| 229. C89 | #18287 | semidirect |
| 308. C24 | Dic356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152224 | 2 |
| #26031027 | 2 |
| #26026057 | 2 |
| #26019279 | 2 |
| #26019211 | 2 |
| #26018825 | 2 |
| C2×#323×C89 | 2 |
| #18287 | 89 |