Finite Group DatabasebetaFinite Group DatabasebetaOrder 14656.
104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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. #20301076 | C2 | semidirect |
| 2. #20301075 | C2 | semidirect |
| 3. #20301059 | C2 | semidirect |
| 4. #20301053 | C2 | semidirect |
| 5. #20301052 | C2 | semidirect |
| 6. #20301042 | C2 | semidirect |
| 18. #16814656 | C4 | semidirect |
| 19. #16814655 | C4 | semidirect |
| 20. #16814651 | C4 | semidirect |
| 22. SD16×C229 | C4 | semidirect |
| 51. C229 | #444 | semidirect |
| 64. SD16 | #11745021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20301076 | 2 |
| #20301075 | 2 |
| #20301059 | 2 |
| #20301053 | 2 |
| #20301052 | 2 |
| #20301042 | 2 |
| #20301009 | 2 |
| #444 | 229 |