Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1050 conjugacy classes of subgroups; only the 227 normal subgroups are shown.
This group has 1050 conjugacy classes of subgroups — too many to draw. Only its 227 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 |
|---|---|---|
| 20. C22×Q8×C53 | C8 | semidirect |
| 141. C53 | #8303 | semidirect |
| 146. C22×Q8 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274783 | 2 |
| C2×#16810349 | 2 |
| C22×C4×Q8×C53 | 2 |
| #8303 | 53 |