Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2734 conjugacy classes of subgroups; only the 371 normal subgroups are shown.
This group has 2734 conjugacy classes of subgroups — too many to draw. Only its 371 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 |
|---|---|---|
| 3. #20272958 | C2 | semidirect |
| 5. C22×#11719919 | C22 | semidirect |
| 9. #16810479 | C4 | semidirect |
| 10. C2×#13133124 | C22 | semidirect |
| 46. C24×C53 | C4⋊C4 | semidirect |
| 140. C53 | #14673 | semidirect |
| 173. C24 | #11719919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810479 | 2 |
| #20272958 | 2 |
| C2×C53×#379 | 2 |
| #14673 | 53 |