Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
490 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 5. C2×#13133284 | C4 | semidirect |
| 13. #16810378 | C4 | semidirect |
| 14. C53×#336 | C4 | semidirect |
| 197. #336 | #6157 | semidirect |
| 198. C53 | #7039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290572 | 2 |
| #20289893 | 2 |
| #20274694 | 2 |
| #7039 | 53 |