Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 370 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. #20293355 | C2 | semidirect |
| 3. #20292978 | C2 | semidirect |
| 4. #20292976 | C2 | semidirect |
| 5. #20292912 | C2 | semidirect |
| 6. #20292911 | C2 | semidirect |
| 9. C8×Dic214 | C2 | semidirect |
| 95. Dic214 | SD16 | semidirect |
| 119. C107 | #3359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293355 | 2 |
| D4×Dic214 | 2 |
| #20292978 | 2 |
| #20292976 | 2 |
| #20292912 | 2 |
| #20292911 | 2 |
| #20292832 | 2 |
| #20292830 | 2 |
| C8×Dic214 | 2 |
| #20292718 | 2 |
| C4×SD16×C107 | 2 |
| #3359 | 107 |