Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D428 | C2 | semidirect |
| 3. #20292987 | C2 | semidirect |
| 4. #20292974 | C2 | semidirect |
| 5. #20292918 | C2 | semidirect |
| 6. #20292913 | C2 | semidirect |
| 7. #20292843 | C2 | semidirect |
| 9. #20292740 | C2 | semidirect |
| 10. C4×#13133807 | C2 | semidirect |
| 11. #446×C107 | C2 | semidirect |
| 125. C107 | #3373 | semidirect |
| 134. #446 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293362 | 2 |
| Q8×D428 | 2 |
| #20292987 | 2 |
| #20292974 | 2 |
| #20292918 | 2 |
| #20292913 | 2 |
| #20292843 | 2 |
| #20292823 | 2 |
| #20292740 | 2 |
| C4×#13133807 | 2 |
| #446×C107 | 2 |
| #3373 | 107 |