Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
280 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 280 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 |
|---|---|---|
| 10. #16812041 | C4 | semidirect |
| 11. C8×Dic107 | C4 | semidirect |
| 15. #106×C107 | C4 | semidirect |
| 51. C8×C107 | C42 | semidirect |
| 65. Dic107 | #106 | direct (N × H) |
| 72. C107 | C4×#106 | semidirect |
| 85. #106 | Dic107 | direct (N × H) |
| 124. C8 | C4×Dic107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812041 | 2 |
| C2×C8×Dic107 | 2 |
| C4⋊C4×Dic107 | 2 |
| #20292389 | 2 |
| C2×#106×C107 | 2 |
| C4×#106 | 107 |