Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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. #20293184 | C2 | semidirect |
| 3. #20292969 | C2 | semidirect |
| 4. #20292923 | C2 | semidirect |
| 5. #20292918 | C2 | semidirect |
| 6. #20292838 | C2 | semidirect |
| 7. #20292833 | C2 | semidirect |
| 9. #20292735 | C2 | semidirect |
| 10. #20292729 | C2 | semidirect |
| 11. #432×C107 | C2 | semidirect |
| 137. C107 | #3116 | semidirect |
| 148. #432 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293184 | 2 |
| C4×#13133818 | 2 |
| #20292969 | 2 |
| #20292923 | 2 |
| #20292918 | 2 |
| #20292838 | 2 |
| #20292833 | 2 |
| #20292791 | 2 |
| #20292735 | 2 |
| #20292729 | 2 |
| #432×C107 | 2 |
| #3116 | 107 |