Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 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×#16812101 | C2 | semidirect |
| 3. #20292935 | C2 | semidirect |
| 4. #20292928 | C2 | semidirect |
| 5. #20292669 | C2 | semidirect |
| 7. #423×C107 | C2 | semidirect |
| 91. C107 | #3080 | semidirect |
| 97. #423 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812101 | 2 |
| C4×#13133818 | 2 |
| #20292935 | 2 |
| #20292928 | 2 |
| #20292669 | 2 |
| #20292629 | 2 |
| #423×C107 | 2 |
| #3080 | 107 |