Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
590 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 590 conjugacy classes of subgroups — too many to draw. Only its 67 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×#13133134 | C4 | semidirect |
| 12. C2×#100×C53 | C4 | semidirect |
| 176. C2×#100 | Dic53 | semidirect |
| 182. C53 | #7311 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274636 | 2 |
| #20274630 | 2 |
| C53×#1783 | 2 |
| #7311 | 53 |