Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
110 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. #20292380 | C2 | semidirect |
| 3. C4×C16×C107 | C2 | semidirect |
| 14. D856 | C8 | semidirect |
| 50. C107 | #1331 | semidirect |
| 52. C4×C16 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D856 | 2 |
| #20292380 | 2 |
| C4×C16×C107 | 2 |
| #1331 | 107 |