Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
160 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 61 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. C4×Dic428 | C2 | semidirect |
| 3. #20292452 | C2 | semidirect |
| 4. #20292430 | C2 | semidirect |
| 6. #20292403 | C2 | semidirect |
| 10. #16812053 | C4 | semidirect |
| 22. Dic428 | C2×C4 | semidirect |
| 27. C107⋊C16 | C2×C4 | semidirect |
| 68. C107 | #2175 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812053 | 2 |
| C4×Dic428 | 2 |
| #20292452 | 2 |
| #20292430 | 2 |
| #20292428 | 2 |
| #20292403 | 2 |
| C4×D8×C107 | 2 |
| #2175 | 107 |