Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
456 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 131 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 |
|---|---|---|
| 2. #20274515 | C2 | semidirect |
| 3. #20272838 | C2 | semidirect |
| 4. #20272836 | C2 | semidirect |
| 9. #16810413 | C4 | semidirect |
| 10. #16810410 | C4 | semidirect |
| 13. C22×M16×C53 | C4 | semidirect |
| 17. C53×#424 | C4 | semidirect |
| 19. C53×#407 | C4 | semidirect |
| 20. C53×#405 | C4 | semidirect |
| 149. C22×M16 | Dic53 | semidirect |
| 153. #424 | Dic53 | semidirect |
| 157. #407 | Dic53 | semidirect |
| 159. #405 | Dic53 | semidirect |
| 163. C53 | #12624 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276356 | 2 |
| #20274515 | 2 |
| #20272838 | 2 |
| #20272836 | 2 |
| C53×#2930 | 2 |
| #12624 | 53 |