Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
422 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 422 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. C22⋊C16×D53 | C2 | semidirect |
| 3. #20274739 | C2 | semidirect |
| 4. #20272727 | C2 | semidirect |
| 5. #20272725 | C2 | semidirect |
| 6. #20272723 | C2 | semidirect |
| 7. C53×#1348 | C2 | semidirect |
| 8. C2×#13133240 | C4 | semidirect |
| 12. #16810861 | C4 | semidirect |
| 13. #16810860 | C4 | semidirect |
| 17. #16810660 | C4 | semidirect |
| 187. #1348 | D53 | semidirect |
| 217. C53 | #11885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284298 | 2 |
| C22⋊C16×D53 | 2 |
| #20274739 | 2 |
| #20272727 | 2 |
| #20272725 | 2 |
| #20272723 | 2 |
| C53×#1348 | 2 |
| #11885 | 53 |