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×#16812100 | C2 | semidirect |
| 3. #20292936 | C2 | semidirect |
| 4. #20292932 | C2 | semidirect |
| 5. #20292929 | C2 | semidirect |
| 6. #20292925 | C2 | semidirect |
| 7. #20292669 | C2 | semidirect |
| 8. #20292667 | C2 | semidirect |
| 9. #20292650 | C2 | semidirect |
| 136. C107 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812100 | 2 |
| #41×Dic107 | 2 |
| #20292936 | 2 |
| #20292932 | 2 |
| #20292929 | 2 |
| #20292925 | 2 |
| #20292669 | 2 |
| #20292667 | 2 |
| #20292650 | 2 |
| #20292628 | 2 |
| #417×C107 | 2 |
| #3080 | 107 |