Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
316 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 75 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. #26020007 | C2 | semidirect |
| 3. #26018244 | C2 | semidirect |
| 4. #26018238 | C2 | semidirect |
| 5. C89×#2166 | C2 | semidirect |
| 7. #19152000 | C4 | semidirect |
| 8. #19151975 | C4 | semidirect |
| 12. #19151711 | C4 | semidirect |
| 116. #2166 | D89 | semidirect |
| 120. C89 | #11770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030902 | 2 |
| #26020007 | 2 |
| #26018244 | 2 |
| #26018238 | 2 |
| C89×#2166 | 2 |
| #11770 | 89 |