Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1386 conjugacy classes of subgroups; only the 235 normal subgroups are shown.
This group has 1386 conjugacy classes of subgroups — too many to draw. Only its 235 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. #26028887 | C2 | semidirect |
| 3. #26021098 | C2 | semidirect |
| 4. #26021090 | C2 | semidirect |
| 5. #26020178 | C2 | semidirect |
| 6. #26020173 | C2 | semidirect |
| 7. C89×#1783 | C2 | semidirect |
| 16. #19151621 | C22 | semidirect |
| 17. C2×#15667930 | C22 | semidirect |
| 19. C2×#15667928 | C22 | semidirect |
| 21. M16×Dic89 | C22 | semidirect |
| 165. #1783 | D89 | semidirect |
| 166. C89 | #21801 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152165 | 2 |
| #26028887 | 2 |
| #26021098 | 2 |
| #26021090 | 2 |
| #26020178 | 2 |
| #26020173 | 2 |
| C89×#1783 | 2 |
| #21801 | 89 |