Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
334 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20272889 | C2 | semidirect |
| 5. #16811180 | C4 | semidirect |
| 8. #16810977 | C4 | semidirect |
| 13. C4×#11719917 | C4 | semidirect |
| 23. #13133209 | C2×C4 | semidirect |
| 34. C4×#88322 | C2×C4 | semidirect |
| 156. C53 | #13603 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285101 | 2 |
| C2×#16810420 | 2 |
| #20272889 | 2 |
| C2×C53×#354 | 2 |
| #13603 | 53 |