Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
372 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C4⋊#88324 | C4 | semidirect |
| 8. C2×C4×#88324 | C4 | semidirect |
| 13. #16810349 | C4 | semidirect |
| 15. C53×#324 | C4 | semidirect |
| 22. #13133276 | C8 | semidirect |
| 164. #324 | #6157 | semidirect |
| 166. C53 | #7205 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290837 | 2 |
| #20290460 | 2 |
| #20273032 | 2 |
| #7205 | 53 |