Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
174 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 174 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. #20292709 | C2 | semidirect |
| 3. #20292427 | C2 | semidirect |
| 4. C16×Dic107 | C2 | semidirect |
| 5. #366×C107 | C2 | semidirect |
| 8. D1712 | C4 | semidirect |
| 17. D856 | C2×C4 | semidirect |
| 24. C16×C107 | C2×C4 | semidirect |
| 44. Dic107 | D16 | semidirect |
| 50. C107 | C4×D16 | semidirect |
| 53. #366 | D107 | semidirect |
| 74. C16 | C4×D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D1712 | 2 |
| #20292709 | 2 |
| #20292427 | 2 |
| C16×Dic107 | 2 |
| #366×C107 | 2 |
| C4×D16 | 107 |