Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16812142 | C2 | semidirect |
| 3. #20293203 | C2 | semidirect |
| 4. #20293107 | C2 | semidirect |
| 5. #20292850 | C2 | semidirect |
| 6. #20292843 | C2 | semidirect |
| 7. #20292838 | C2 | semidirect |
| 8. #20292833 | C2 | semidirect |
| 9. #20292629 | C2 | semidirect |
| 10. C2×#16812034 | C2 | semidirect |
| 11. #424×C107 | C2 | semidirect |
| 147. C107 | #3046 | semidirect |
| 156. #424 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812142 | 2 |
| C2×#16812131 | 2 |
| #20293203 | 2 |
| #20293107 | 2 |
| #20292850 | 2 |
| #20292843 | 2 |
| #20292838 | 2 |
| #20292833 | 2 |
| #20292629 | 2 |
| C2×#16812034 | 2 |
| #424×C107 | 2 |
| #3046 | 107 |