Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1306 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 232 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. #20291391 | C2 | semidirect |
| 2. #20290194 | C2 | semidirect |
| 3. #20290174 | C2 | semidirect |
| 5. #16811644 | C22 | semidirect |
| 6. #16811643 | C22 | semidirect |
| 11. C4×#11719940 | C22 | semidirect |
| 12. #16811478 | C22 | semidirect |
| 29. #13133272 | C23 | semidirect |
| 204. C53 | #17666 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291391 | 2 |
| #20290194 | 2 |
| #20290174 | 2 |
| C22×#13133204 | 2 |
| #17666 | 53 |