Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 3. #20292933 | C2 | semidirect |
| 4. #20292932 | C2 | semidirect |
| 5. #20292919 | C2 | semidirect |
| 6. #20292913 | C2 | semidirect |
| 7. #20292912 | C2 | semidirect |
| 11. #477×C107 | C2 | semidirect |
| 47. Q8×D107 | Q8 | semidirect |
| 131. C107 | #3078 | semidirect |
| 137. #477 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293182 | 2 |
| C4×Q8×D107 | 2 |
| #20292933 | 2 |
| #20292932 | 2 |
| #20292919 | 2 |
| #20292913 | 2 |
| #20292912 | 2 |
| #20292668 | 2 |
| #20292649 | 2 |
| #20292634 | 2 |
| #477×C107 | 2 |
| #3078 | 107 |