Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. C2×C8×Dic107 | C2 | semidirect |
| 5. #20292391 | C2 | semidirect |
| 6. #20292386 | C2 | semidirect |
| 7. #424×C107 | C2 | semidirect |
| 13. #16812032 | C4 | semidirect |
| 14. #16812029 | C4 | semidirect |
| 91. C107 | #1937 | semidirect |
| 92. #424 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812035 | 2 |
| #20292621 | 2 |
| #20292593 | 2 |
| C2×C8×Dic107 | 2 |
| #20292391 | 2 |
| #20292386 | 2 |
| #424×C107 | 2 |
| #1937 | 107 |