Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. #20300987 | C2 | semidirect |
| 2. #20300986 | C2 | semidirect |
| 3. #20300983 | C2 | semidirect |
| 4. #20300983 | C2 | semidirect |
| 5. #20300981 | C2 | semidirect |
| 6. #20300981 | C2 | semidirect |
| 7. #20300979 | C2 | semidirect |
| 8. #20300978 | C2 | semidirect |
| 12. #20300967 | C2 | semidirect |
| 13. #20300966 | C2 | semidirect |
| 14. #20300964 | C2 | semidirect |
| 15. C22⋊Q8×C229 | C2 | semidirect |
| 97. C229 | #563 | semidirect |
| 113. C22⋊Q8 | D229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300987 | 2 |
| #20300986 | 2 |
| #20300983 | 2 |
| #20300981 | 2 |
| #20300979 | 2 |
| #20300978 | 2 |
| #20300974 | 2 |
| #20300971 | 2 |
| #20300970 | 2 |
| #20300967 | 2 |
| #20300966 | 2 |
| #20300964 | 2 |
| C22⋊Q8×C229 | 2 |
| #563 | 229 |