Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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. #20293352 | C2 | semidirect |
| 3. #20292976 | C2 | semidirect |
| 4. #20292910 | C2 | semidirect |
| 5. #20292909 | C2 | semidirect |
| 8. C8×Dic214 | C2 | semidirect |
| 11. #487×C107 | C2 | semidirect |
| 95. Dic214 | SD16 | semidirect |
| 119. C107 | #3359 | semidirect |
| 123. #487 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293352 | 2 |
| #20293292 | 2 |
| #20292976 | 2 |
| #20292910 | 2 |
| #20292909 | 2 |
| #20292831 | 2 |
| #20292829 | 2 |
| C8×Dic214 | 2 |
| C4×#13133807 | 2 |
| #20292712 | 2 |
| #487×C107 | 2 |
| #3359 | 107 |