Finite Group DatabasebetaFinite Group DatabasebetaOrder 13696.
764 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 293 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. C22×#13133802 | C2 | semidirect |
| 2. #20292594 | C2 | semidirect |
| 3. #20292591 | C2 | semidirect |
| 7. C2×#13133802 | C22 | semidirect |
| 8. C22×C107⋊C8 | C22 | semidirect |
| 9. C22⋊(C107⋊C8) | C22 | semidirect |
| 84. C107 | #2879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133802 | 2 |
| #20292594 | 2 |
| #20292591 | 2 |
| C22×#41×C107 | 2 |
| #2879 | 107 |