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×#16812132 | C2 | semidirect |
| 2. #20293178 | C2 | semidirect |
| 3. C4×#13133819 | C2 | semidirect |
| 4. #20292851 | C2 | semidirect |
| 5. #20292845 | C2 | semidirect |
| 6. #20292829 | C2 | semidirect |
| 7. #20292827 | C2 | semidirect |
| 8. #20292823 | C2 | semidirect |
| 9. C4⋊C8×D107 | C2 | semidirect |
| 10. #20292622 | C2 | semidirect |
| 11. #462×C107 | C2 | semidirect |
| 47. #13133819 | D4 | semidirect |
| 137. C4×C107 | #135 | semidirect |
| 151. C107 | #3035 | semidirect |
| 157. #462 | D107 | semidirect |
| 292. C4 | #16812132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812132 | 2 |
| #20293178 | 2 |
| C4×#13133819 | 2 |
| #20292851 | 2 |
| #20292845 | 2 |
| #20292829 | 2 |
| #20292827 | 2 |
| #20292823 | 2 |
| C4⋊C8×D107 | 2 |
| #20292622 | 2 |
| #462×C107 | 2 |
| #3035 | 107 |