Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
290 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16812040 | C2 | semidirect |
| 5. #20292389 | C2 | semidirect |
| 6. #20292382 | C2 | semidirect |
| 7. C4×C4⋊C4×C107 | C2 | semidirect |
| 16. #16812029 | C4 | semidirect |
| 119. C107 | #1926 | semidirect |
| 124. C4×C4⋊C4 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812040 | 2 |
| C2×#16812029 | 2 |
| #20292529 | 2 |
| #20292389 | 2 |
| #20292382 | 2 |
| C4×C4⋊C4×C107 | 2 |
| #1926 | 107 |