Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20293255 | C2 | semidirect |
| 4. #20292395 | C2 | semidirect |
| 5. #20292388 | C2 | semidirect |
| 6. #20292386 | C2 | semidirect |
| 49. C2×D4×C107 | Q8 | semidirect |
| 113. C107 | #2027 | semidirect |
| 145. C2×D4 | Dic214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293255 | 2 |
| #20292632 | 2 |
| #20292530 | 2 |
| #20292395 | 2 |
| #20292388 | 2 |
| #20292386 | 2 |
| #418×C107 | 2 |
| #2027 | 107 |