Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 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. #20293350 | C2 | semidirect |
| 2. Q8×D428 | C2 | semidirect |
| 3. #20292987 | C2 | semidirect |
| 4. #20292978 | C2 | semidirect |
| 5. #20292923 | C2 | semidirect |
| 6. #20292908 | C2 | semidirect |
| 8. #20292833 | C2 | semidirect |
| 9. #20292729 | C2 | semidirect |
| 11. #446×C107 | C2 | semidirect |
| 123. C107 | #3367 | semidirect |
| 132. #446 | D107 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293350 | 2 |
| Q8×D428 | 2 |
| #20292987 | 2 |
| #20292978 | 2 |
| #20292923 | 2 |
| #20292908 | 2 |
| #20292843 | 2 |
| #20292833 | 2 |
| #20292729 | 2 |
| C4×D856 | 2 |
| #446×C107 | 2 |
| #3367 | 107 |