Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20273214 | C2 | semidirect |
| 5. #20272617 | C2 | semidirect |
| 6. #20272573 | C2 | semidirect |
| 7. C53×#1518 | C2 | semidirect |
| 11. #16810910 | C4 | semidirect |
| 12. #16810900 | C4 | semidirect |
| 49. C4⋊#88322 | C2×C4 | semidirect |
| 57. C4⋊Q8×C53 | C2×C4 | semidirect |
| 58. C4⋊Q8×C53 | C2×C4 | semidirect |
| 192. #1518 | D53 | semidirect |
| 224. C53 | #9175 | semidirect |
| 229. C4⋊Q8 | C4×D53 | semidirect |
| 230. C4⋊Q8 | C4×D53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284508 | 2 |
| #20277623 | 2 |
| #20273214 | 2 |
| #20273107 | 2 |
| #20272617 | 2 |
| #20272573 | 2 |
| C53×#1518 | 2 |
| #9175 | 53 |