Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 2. #20292913 | C2 | semidirect |
| 4. C8×Dic214 | C2 | semidirect |
| 5. #20292372 | C2 | semidirect |
| 7. #334×C107 | C2 | semidirect |
| 57. Dic214 | SD16 | semidirect |
| 61. C8×C107 | SD16 | semidirect |
| 80. C107 | #1666 | semidirect |
| 85. #334 | D107 | semidirect |
| 142. C8 | #13133807 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293000 | 2 |
| #20292913 | 2 |
| #20292828 | 2 |
| C8×Dic214 | 2 |
| #20292372 | 2 |
| #20292370 | 2 |
| #334×C107 | 2 |
| #1666 | 107 |