Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. #20293255 | C2 | semidirect |
| 2. #20292995 | C2 | semidirect |
| 3. #20292986 | C2 | semidirect |
| 4. #20292981 | C2 | semidirect |
| 5. #20292977 | C2 | semidirect |
| 6. #20292636 | C2 | semidirect |
| 9. C2×#16812033 | C2 | semidirect |
| 10. #20292583 | C2 | semidirect |
| 128. C107 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293255 | 2 |
| #20292995 | 2 |
| #20292986 | 2 |
| #20292981 | 2 |
| #20292977 | 2 |
| #20292636 | 2 |
| #20292628 | 2 |
| #20292623 | 2 |
| C2×#16812033 | 2 |
| #20292583 | 2 |
| #536×C107 | 2 |
| #3137 | 107 |