Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
232 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 232 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 |
|---|---|---|
| 8. #16812045 | C4 | semidirect |
| 9. #16812043 | C4 | semidirect |
| 10. #16812041 | C4 | semidirect |
| 16. C4×C8×C107 | C4 | semidirect |
| 65. C107 | #1772 | semidirect |
| 81. C4×C8 | Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812045 | 2 |
| #20292665 | 2 |
| #20292582 | 2 |
| #20292387 | 2 |
| C2×C4×C8×C107 | 2 |
| #1772 | 107 |