Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 82 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. #20290188 | C2 | semidirect |
| 4. #20290098 | C2 | semidirect |
| 5. #20289608 | C2 | semidirect |
| 6. #20289567 | C2 | semidirect |
| 25. #16810904 | C4 | semidirect |
| 26. #16810903 | C4 | semidirect |
| 27. #16810825 | C4 | semidirect |
| 32. C53×#461 | C4 | semidirect |
| 224. #461 | #6157 | semidirect |
| 243. C53 | #9165 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291575 | 2 |
| #20290485 | 2 |
| #20290188 | 2 |
| #20290098 | 2 |
| #20289608 | 2 |
| #20289567 | 2 |
| #20284813 | 2 |
| #9165 | 53 |