Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1114 conjugacy classes of subgroups; only the 380 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 380 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. #20291682 | C2 | semidirect |
| 2. C2×#16811681 | C2 | semidirect |
| 3. #20290957 | C2 | semidirect |
| 4. C2×#16811521 | C2 | semidirect |
| 8. C2×#13133291 | C22 | semidirect |
| 9. C2×#13133291 | C22 | semidirect |
| 10. C22×#11719910 | C22 | semidirect |
| 11. #16811521 | C22 | semidirect |
| 12. #16811521 | C22 | semidirect |
| 134. C53 | #33340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291682 | 2 |
| C2×#16811681 | 2 |
| #20290957 | 2 |
| C2×#16811521 | 2 |
| #20289427 | 2 |
| #33340 | 53 |