Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
324 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 63 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. #20276524 | C2 | semidirect |
| 3. #20274865 | C2 | semidirect |
| 4. #20272705 | C2 | semidirect |
| 5. #20272701 | C2 | semidirect |
| 6. #20272700 | C2 | semidirect |
| 7. C53×#1341 | C2 | semidirect |
| 9. #16811020 | C4 | semidirect |
| 10. #16810998 | C4 | semidirect |
| 14. #16810735 | C4 | semidirect |
| 15. #16810734 | C4 | semidirect |
| 148. #1341 | D53 | semidirect |
| 175. C53 | #11837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285448 | 2 |
| #20276524 | 2 |
| #20274865 | 2 |
| #20272705 | 2 |
| #20272701 | 2 |
| #20272700 | 2 |
| C53×#1341 | 2 |
| #11837 | 53 |