Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
818 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26020333 | C2 | semidirect |
| 3. #26020327 | C2 | semidirect |
| 4. #26018782 | C2 | semidirect |
| 5. #26018781 | C2 | semidirect |
| 6. #26018780 | C2 | semidirect |
| 7. C89×#1510 | C2 | semidirect |
| 12. C2×#15668008 | C4 | semidirect |
| 13. C2×#15668003 | C4 | semidirect |
| 19. C2×D4×Dic89 | C4 | semidirect |
| 20. C2×#15667974 | C4 | semidirect |
| 268. #1510 | D89 | semidirect |
| 269. C89 | #8518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152201 | 2 |
| #26020333 | 2 |
| #26020327 | 2 |
| #26018782 | 2 |
| #26018781 | 2 |
| #26018780 | 2 |
| C89×#1510 | 2 |
| #8518 | 89 |