Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20293425 | C2 | semidirect |
| 2. C2×#16812135 | C2 | semidirect |
| 3. #20292644 | C2 | semidirect |
| 4. #20292632 | C2 | semidirect |
| 5. #20292600 | C2 | semidirect |
| 6. #20292397 | C2 | semidirect |
| 7. #535×C107 | C2 | semidirect |
| 35. C2×Dic214 | D4 | semidirect |
| 36. C2×D428 | D4 | semidirect |
| 48. #13133802 | D4 | semidirect |
| 50. C2×C107⋊C8 | D4 | semidirect |
| 143. C107 | #2008 | semidirect |
| 146. #535 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293425 | 2 |
| C2×#16812135 | 2 |
| #20292644 | 2 |
| #20292632 | 2 |
| #20292600 | 2 |
| #20292397 | 2 |
| #535×C107 | 2 |
| #2008 | 107 |