Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C2×#16812032 | C2 | semidirect |
| 5. C2×#16812027 | C2 | semidirect |
| 6. #20292391 | C2 | semidirect |
| 7. #343×C107 | C2 | semidirect |
| 11. #16812142 | C4 | semidirect |
| 117. C107 | #1908 | semidirect |
| 123. #343 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812142 | 2 |
| C2×#16812117 | 2 |
| #20292626 | 2 |
| C2×#16812032 | 2 |
| C2×#16812027 | 2 |
| #20292391 | 2 |
| #343×C107 | 2 |
| #1908 | 107 |