Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #20293362 | C2 | semidirect |
| 2. D4×Dic214 | C2 | semidirect |
| 3. #20292988 | C2 | semidirect |
| 4. #20292974 | C2 | semidirect |
| 5. #20292916 | C2 | semidirect |
| 6. #20292912 | C2 | semidirect |
| 7. #20292844 | C2 | semidirect |
| 9. #20292757 | C2 | semidirect |
| 10. #20292736 | C2 | semidirect |
| 11. C4×SD16×C107 | C2 | semidirect |
| 125. C107 | #3373 | semidirect |
| 136. C4×SD16 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293362 | 2 |
| D4×Dic214 | 2 |
| #20292988 | 2 |
| #20292974 | 2 |
| #20292916 | 2 |
| #20292912 | 2 |
| #20292844 | 2 |
| #20292822 | 2 |
| #20292757 | 2 |
| #20292736 | 2 |
| C4×SD16×C107 | 2 |
| #3373 | 107 |