Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
174 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 65 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×D856 | C2 | semidirect |
| 3. #20292453 | C2 | semidirect |
| 4. #20292429 | C2 | semidirect |
| 5. C4×C16×C107 | C2 | semidirect |
| 8. D1712 | C4 | direct (N × H) |
| 17. D856 | C2×C4 | semidirect |
| 24. C16×C107 | C2×C4 | semidirect |
| 41. C4×C107 | D16 | semidirect |
| 50. C107 | C4×D16 | semidirect |
| 55. C4×C16 | D107 | semidirect |
| 74. C16 | C4×D107 | semidirect |
| 92. C4 | D1712 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D1712 | 2 |
| C4×D856 | 2 |
| #20292453 | 2 |
| #20292429 | 2 |
| C4×C16×C107 | 2 |
| C4×D16 | 107 |