Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20292743 | C2 | semidirect |
| 3. #20292433 | C2 | semidirect |
| 4. C16×Dic107 | C2 | semidirect |
| 5. #368×C107 | C2 | semidirect |
| 8. Dic856 | C4 | semidirect |
| 9. #16812054 | C4 | semidirect |
| 10. D1712 | C4 | semidirect |
| 50. C107 | #2178 | semidirect |
| 53. #368 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293059 | 2 |
| #20292743 | 2 |
| #20292433 | 2 |
| C16×Dic107 | 2 |
| #368×C107 | 2 |
| #2178 | 107 |