Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
846 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 846 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26020351 | C2 | semidirect |
| 3. C4×#15667926 | C2 | semidirect |
| 4. #26018769 | C2 | semidirect |
| 5. #26018767 | C2 | semidirect |
| 6. #26018588 | C2 | semidirect |
| 7. C89×#1826 | C2 | semidirect |
| 12. C2×#15668011 | C4 | semidirect |
| 15. C2×#15667987 | C4 | semidirect |
| 18. C2×#15667974 | C4 | semidirect |
| 20. C2×#15667970 | C4 | semidirect |
| 279. #1826 | D89 | semidirect |
| 284. C89 | #8360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152311 | 2 |
| #26020351 | 2 |
| C4×#15667926 | 2 |
| #26018769 | 2 |
| #26018767 | 2 |
| #26018588 | 2 |
| C89×#1826 | 2 |
| #8360 | 89 |