Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 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 |
|---|---|---|
| 1. C2×#16812130 | C2 | semidirect |
| 2. #20293175 | C2 | semidirect |
| 3. C4×#13133819 | C2 | semidirect |
| 4. #20292847 | C2 | semidirect |
| 5. #20292841 | C2 | semidirect |
| 6. #20292837 | C2 | semidirect |
| 7. #20292833 | C2 | semidirect |
| 8. #20292819 | C2 | semidirect |
| 9. C4⋊C8×D107 | C2 | semidirect |
| 10. #20292620 | C2 | semidirect |
| 11. #460×C107 | C2 | semidirect |
| 45. #13133819 | D4 | semidirect |
| 136. C4×C107 | #135 | semidirect |
| 151. C107 | #3035 | semidirect |
| 159. #460 | D107 | semidirect |
| 292. C4 | #16812130 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812130 | 2 |
| #20293175 | 2 |
| C4×#13133819 | 2 |
| #20292847 | 2 |
| #20292841 | 2 |
| #20292837 | 2 |
| #20292833 | 2 |
| #20292819 | 2 |
| C4⋊C8×D107 | 2 |
| #20292620 | 2 |
| #460×C107 | 2 |
| #3035 | 107 |