Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
784 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #20272834 | C2 | semidirect |
| 5. C22×C22⋊Dic53 | C4 | semidirect |
| 6. C22×C22⋊Dic53 | C4 | semidirect |
| 11. #16810503 | C4 | semidirect |
| 214. C53 | #12854 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20277293 | 2 |
| #20274630 | 2 |
| #20272834 | 2 |
| C53×#1783 | 2 |
| #12854 | 53 |