Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16812109 | C2 | semidirect |
| 3. #20292923 | C2 | semidirect |
| 4. #20292918 | C2 | semidirect |
| 5. #20292913 | C2 | semidirect |
| 6. #20292908 | C2 | semidirect |
| 7. #20292669 | C2 | semidirect |
| 9. #423×C107 | C2 | semidirect |
| 36. #13133818 | Q8 | semidirect |
| 89. D428 | C2×Q8 | semidirect |
| 96. Dic214 | C2×Q8 | semidirect |
| 122. C107 | #3079 | semidirect |
| 130. #423 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812109 | 2 |
| C4×#13133818 | 2 |
| #20292923 | 2 |
| #20292918 | 2 |
| #20292913 | 2 |
| #20292908 | 2 |
| #20292669 | 2 |
| #20292629 | 2 |
| #423×C107 | 2 |
| #3079 | 107 |