Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
412 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 97 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. #20273506 | C2 | semidirect |
| 5. #20272547 | C2 | semidirect |
| 6. #20272547 | C2 | semidirect |
| 7. C53×#1574 | C2 | semidirect |
| 20. #16810371 | C4 | semidirect |
| 21. #16810371 | C4 | semidirect |
| 22. #16810366 | C4 | semidirect |
| 23. #16810366 | C4 | semidirect |
| 161. #1574 | D53 | semidirect |
| 191. C53 | #8934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283781 | 2 |
| #20275542 | 2 |
| #20273506 | 2 |
| #20273375 | 2 |
| #20272547 | 2 |
| C53×#1574 | 2 |
| #8934 | 53 |