Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
340 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20293352 | C2 | semidirect |
| 3. #20292994 | C2 | semidirect |
| 4. #20292977 | C2 | semidirect |
| 5. #20292936 | C2 | semidirect |
| 6. #20292923 | C2 | semidirect |
| 8. #20292754 | C2 | semidirect |
| 117. C107 | #3372 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293352 | 2 |
| #20293334 | 2 |
| #20292994 | 2 |
| #20292977 | 2 |
| #20292936 | 2 |
| #20292923 | 2 |
| #20292830 | 2 |
| #20292754 | 2 |
| #20292728 | 2 |
| C4×#13133806 | 2 |
| #461×C107 | 2 |
| #3372 | 107 |