Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #20293031 | C2 | semidirect |
| 3. #20292452 | C2 | semidirect |
| 4. Dic107⋊C16 | C2 | semidirect |
| 7. #366×C107 | C2 | semidirect |
| 23. D856 | Q8 | semidirect |
| 64. C107 | #2224 | semidirect |
| 68. #366 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293031 | 2 |
| #20292709 | 2 |
| #20292452 | 2 |
| Dic107⋊C16 | 2 |
| #20292429 | 2 |
| #20292427 | 2 |
| #366×C107 | 2 |
| #2224 | 107 |