Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic214 | C2 | semidirect |
| 2. C2×#16812139 | C2 | semidirect |
| 3. #20292782 | C2 | semidirect |
| 4. #20292765 | C2 | semidirect |
| 5. #20292635 | C2 | semidirect |
| 6. #20292591 | C2 | semidirect |
| 15. C2×#13133808 | C22 | semidirect |
| 16. C2×#13133806 | C22 | semidirect |
| 18. #16812032 | C22 | semidirect |
| 34. C2×Dic214 | D4 | semidirect |
| 95. C22×C107 | #137 | semidirect |
| 109. C107 | #3004 | semidirect |
| 204. C22 | #16812139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic214 | 2 |
| C2×#16812139 | 2 |
| #20292782 | 2 |
| #20292765 | 2 |
| #20292635 | 2 |
| #20292591 | 2 |
| #525×C107 | 2 |
| #3004 | 107 |