Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
392 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20273480 | C2 | semidirect |
| 5. #20272609 | C2 | semidirect |
| 6. #20272607 | C2 | semidirect |
| 7. C53×#1569 | C2 | semidirect |
| 22. #16810362 | C4 | semidirect |
| 23. #16810362 | C4 | semidirect |
| 24. #16810362 | C4 | semidirect |
| 25. #16810362 | C4 | semidirect |
| 184. #1569 | D53 | semidirect |
| 217. C53 | #8918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283785 | 2 |
| #20275546 | 2 |
| #20273480 | 2 |
| #20273306 | 2 |
| #20272609 | 2 |
| #20272607 | 2 |
| C53×#1569 | 2 |
| #8918 | 53 |