Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
212 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 18. #16812027 | C4 | semidirect |
| 94. C107 | #1930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20292667 | 2 |
| #20292637 | 2 |
| C2×#16812032 | 2 |
| C2×#16812027 | 2 |
| #20292585 | 2 |
| #20292391 | 2 |
| #343×C107 | 2 |
| #1930 | 107 |