Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
458 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 78 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×#13133272 | C4 | semidirect |
| 13. #16810378 | C4 | semidirect |
| 14. C53×#336 | C4 | semidirect |
| 164. #336 | #6157 | semidirect |
| 165. C53 | #7036 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290442 | 2 |
| #20289891 | 2 |
| #20274476 | 2 |
| #7036 | 53 |