Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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. #20300996 | C2 | semidirect |
| 3. #20300995 | C2 | semidirect |
| 4. #20300923 | C2 | semidirect |
| 5. #20300916 | C2 | semidirect |
| 6. #20300899 | C2 | semidirect |
| 7. #104×C229 | C2 | semidirect |
| 9. #16814656 | C4 | semidirect |
| 10. #16814654 | C4 | semidirect |
| 11. #16814653 | C4 | semidirect |
| 12. #16814651 | C4 | semidirect |
| 51. C229 | #444 | semidirect |
| 58. #104 | D229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20301008 | 2 |
| #20300996 | 2 |
| #20300995 | 2 |
| #20300923 | 2 |
| #20300916 | 2 |
| #20300899 | 2 |
| #104×C229 | 2 |
| #444 | 229 |