Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
178 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 53 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. C2×Dic856 | C2 | semidirect |
| 2. C2×#16812055 | C2 | semidirect |
| 5. #20293005 | C2 | semidirect |
| 6. #20292402 | C2 | semidirect |
| 74. C107 | #2251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic856 | 2 |
| C2×#16812055 | 2 |
| C2×#16812053 | 2 |
| #20293010 | 2 |
| #20293005 | 2 |
| #20292402 | 2 |
| C2×SD32×C107 | 2 |
| #2251 | 107 |