Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20293347 | C2 | semidirect |
| 2. D4×Dic214 | C2 | semidirect |
| 3. #20292985 | C2 | semidirect |
| 4. #20292978 | C2 | semidirect |
| 5. #20292921 | C2 | semidirect |
| 6. #20292907 | C2 | semidirect |
| 8. #20292832 | C2 | semidirect |
| 9. #20292757 | C2 | semidirect |
| 10. #20292724 | C2 | semidirect |
| 123. C107 | #3367 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293347 | 2 |
| D4×Dic214 | 2 |
| #20292985 | 2 |
| #20292978 | 2 |
| #20292921 | 2 |
| #20292907 | 2 |
| #20292840 | 2 |
| #20292832 | 2 |
| #20292757 | 2 |
| #20292724 | 2 |
| C4×D8×C107 | 2 |
| #3367 | 107 |