Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16812108 | C2 | semidirect |
| 3. #20292921 | C2 | semidirect |
| 4. #20292916 | C2 | semidirect |
| 5. #20292911 | C2 | semidirect |
| 6. #20292906 | C2 | semidirect |
| 7. #20292670 | C2 | semidirect |
| 8. #20292650 | C2 | semidirect |
| 11. #428×C107 | C2 | semidirect |
| 44. #13133818 | Q8 | semidirect |
| 104. D428 | C2×Q8 | semidirect |
| 111. Dic214 | C2×Q8 | semidirect |
| 139. C107 | #3079 | semidirect |
| 147. #428 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16812108 | 2 |
| #20293095 | 2 |
| #20292921 | 2 |
| #20292916 | 2 |
| #20292911 | 2 |
| #20292906 | 2 |
| #20292670 | 2 |
| #20292650 | 2 |
| #20292629 | 2 |
| #20292626 | 2 |
| #428×C107 | 2 |
| #3079 | 107 |