Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
452 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 87 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. #20276390 | C2 | semidirect |
| 5. #20274759 | C2 | semidirect |
| 6. #20274518 | C2 | semidirect |
| 7. C53×#2123 | C2 | semidirect |
| 8. C22×#11719924 | C4 | semidirect |
| 16. #16810659 | C4 | semidirect |
| 17. #16810632 | C4 | semidirect |
| 18. #16810627 | C4 | semidirect |
| 210. #2123 | D53 | semidirect |
| 243. C53 | #13229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284356 | 2 |
| #20276390 | 2 |
| #20276386 | 2 |
| #20276366 | 2 |
| #20274759 | 2 |
| #20274518 | 2 |
| C53×#2123 | 2 |
| #13229 | 53 |