Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
290 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 95 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×#16812041 | C2 | semidirect |
| 5. C4×C4⋊Dic107 | C2 | semidirect |
| 6. #20292390 | C2 | semidirect |
| 7. #336×C107 | C2 | semidirect |
| 17. #16812031 | C4 | semidirect |
| 119. C107 | #1926 | semidirect |
| 126. #336 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812041 | 2 |
| C2×#16812031 | 2 |
| #20292529 | 2 |
| C4×C4⋊Dic107 | 2 |
| #20292390 | 2 |
| #336×C107 | 2 |
| #1926 | 107 |