Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×C4×Dic214 | C2 | semidirect |
| 2. #20292960 | C2 | semidirect |
| 4. #20292931 | C2 | semidirect |
| 5. #20292846 | C2 | semidirect |
| 6. #20292782 | C2 | semidirect |
| 8. #20292732 | C2 | semidirect |
| 9. #20292727 | C2 | semidirect |
| 10. #20292684 | C2 | semidirect |
| 132. C107 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic214 | 2 |
| #20292960 | 2 |
| #20292943 | 2 |
| #20292931 | 2 |
| #20292846 | 2 |
| #20292782 | 2 |
| #20292765 | 2 |
| #20292732 | 2 |
| #20292727 | 2 |
| #20292684 | 2 |
| #529×C107 | 2 |
| #3117 | 107 |