Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
162 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20292721 | C2 | semidirect |
| 4. #20292454 | C2 | semidirect |
| 5. #20292432 | C2 | semidirect |
| 6. C16×Dic107 | C2 | semidirect |
| 11. #16812053 | C4 | semidirect |
| 23. Dic428 | C2×C4 | semidirect |
| 30. C107⋊C16 | C2×C4 | semidirect |
| 62. Dic107 | SD32 | semidirect |
| 68. C107 | C4×SD32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812053 | 2 |
| #20292721 | 2 |
| D8×Dic107 | 2 |
| #20292454 | 2 |
| #20292432 | 2 |
| C16×Dic107 | 2 |
| #357×C107 | 2 |
| C4×SD32 | 107 |