Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20293298 | C2 | semidirect |
| 2. D4×Dic214 | C2 | semidirect |
| 3. #20292974 | C2 | semidirect |
| 4. #20292972 | C2 | semidirect |
| 5. #20292907 | C2 | semidirect |
| 6. #20292906 | C2 | semidirect |
| 7. #20292822 | C2 | semidirect |
| 8. #20292820 | C2 | semidirect |
| 9. C8×Dic214 | C2 | semidirect |
| 10. #20292707 | C2 | semidirect |
| 11. C4×D8×C107 | C2 | semidirect |
| 81. D4×C107 | #41 | semidirect |
| 102. Dic214 | D8 | semidirect |
| 132. C107 | #3358 | semidirect |
| 143. C4×D8 | D107 | semidirect |
| 222. D4 | #13133818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293298 | 2 |
| D4×Dic214 | 2 |
| #20292974 | 2 |
| #20292972 | 2 |
| #20292907 | 2 |
| #20292906 | 2 |
| #20292822 | 2 |
| #20292820 | 2 |
| C8×Dic214 | 2 |
| #20292707 | 2 |
| C4×D8×C107 | 2 |
| #3358 | 107 |