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. #20292744 | C2 | semidirect |
| 3. #20292743 | C2 | semidirect |
| 4. #20292456 | C2 | semidirect |
| 5. #20292435 | C2 | semidirect |
| 6. C16×Dic107 | C2 | semidirect |
| 7. #359×C107 | C2 | semidirect |
| 11. #16812055 | C4 | semidirect |
| 12. #16812053 | C4 | semidirect |
| 13. #16812052 | C4 | semidirect |
| 14. #16812050 | C4 | semidirect |
| 72. C107 | #2178 | semidirect |
| 78. #359 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293057 | 2 |
| #20292744 | 2 |
| #20292743 | 2 |
| #20292456 | 2 |
| #20292435 | 2 |
| C16×Dic107 | 2 |
| #359×C107 | 2 |
| #2178 | 107 |