Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 83 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. C4×#13133132 | C2 | semidirect |
| 3. #20272740 | C2 | semidirect |
| 4. #20272713 | C2 | semidirect |
| 5. C53×#1460 | C2 | semidirect |
| 6. C2×#13133191 | C4 | semidirect |
| 8. #16810562 | C4 | semidirect |
| 10. #16810540 | C4 | semidirect |
| 16. #16810486 | C4 | semidirect |
| 190. #1460 | D53 | semidirect |
| 218. C53 | #11729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20280599 | 2 |
| C4×#13133132 | 2 |
| #20272740 | 2 |
| #20272713 | 2 |
| C53×#1460 | 2 |
| #11729 | 53 |