Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20293007 | C2 | semidirect |
| 4. #20292372 | C2 | semidirect |
| 5. #334×C107 | C2 | semidirect |
| 62. C107 | #1689 | semidirect |
| 66. #334 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293007 | 2 |
| #20292908 | 2 |
| #20292706 | 2 |
| #20292372 | 2 |
| #334×C107 | 2 |
| #1689 | 107 |