Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
460 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 121 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. #20274517 | C2 | semidirect |
| 4. #20272843 | C2 | semidirect |
| 6. C2×#13133224 | C4 | semidirect |
| 10. #16810647 | C4 | semidirect |
| 12. #16810590 | C4 | semidirect |
| 15. C2×C4×#88322 | C4 | semidirect |
| 16. #16810422 | C4 | semidirect |
| 17. #16810420 | C4 | semidirect |
| 174. C53 | #12633 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283427 | 2 |
| #20276400 | 2 |
| #20274517 | 2 |
| #20272843 | 2 |
| C53×#2126 | 2 |
| #12633 | 53 |