Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
388 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 388 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. #20272885 | C2 | semidirect |
| 5. #16811180 | C4 | semidirect |
| 6. #16810987 | C4 | semidirect |
| 13. C4×#11719917 | C4 | semidirect |
| 22. #13133209 | C2×C4 | semidirect |
| 33. #13133128 | C2×C4 | semidirect |
| 170. C53 | #13595 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285089 | 2 |
| C2×#16810416 | 2 |
| #20272885 | 2 |
| C2×C53×#353 | 2 |
| #13595 | 53 |