Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
142 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. #20292735 | C2 | semidirect |
| 3. #20292451 | C2 | semidirect |
| 4. #20292442 | C2 | semidirect |
| 6. #20292405 | C2 | semidirect |
| 10. #16812055 | C4 | semidirect |
| 11. #16812053 | C4 | semidirect |
| 65. C107 | #2180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20293067 | 2 |
| #20292735 | 2 |
| #20292451 | 2 |
| #20292442 | 2 |
| #20292437 | 2 |
| #20292405 | 2 |
| #444×C107 | 2 |
| #2180 | 107 |