Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
252 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 3. #20292359 | C2 | semidirect |
| 57. Dic214 | M16 | semidirect |
| 77. C107 | #1491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic214 | 2 |
| #20292684 | 2 |
| #20292359 | 2 |
| C4×M16×C107 | 2 |
| #1491 | 107 |