Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
380 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 4. C23×#88322 | C4 | semidirect |
| 7. C2×C22⋊#88322 | C4 | semidirect |
| 14. C53×#323 | C4 | semidirect |
| 22. #13133132 | C8 | semidirect |
| 162. #323 | Dic53 | semidirect |
| 163. C53 | #7204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20275008 | 2 |
| C4×#13133132 | 2 |
| C53×#1460 | 2 |
| #7204 | 53 |