Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
372 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 3. #20292994 | C2 | semidirect |
| 4. #20292985 | C2 | semidirect |
| 5. #20292980 | C2 | semidirect |
| 6. #20292976 | C2 | semidirect |
| 7. #20292635 | C2 | semidirect |
| 9. C2×#16812034 | C2 | semidirect |
| 10. #20292582 | 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 |
| #20293198 | 2 |
| #20292994 | 2 |
| #20292985 | 2 |
| #20292980 | 2 |
| #20292976 | 2 |
| #20292635 | 2 |
| #20292628 | 2 |
| C2×#16812034 | 2 |
| #20292582 | 2 |
| #416×C107 | 2 |
| #3137 | 107 |