Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
454 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 71 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. #20276400 | C2 | semidirect |
| 3. #20272871 | C2 | semidirect |
| 4. C53×#2126 | C2 | semidirect |
| 7. C2×#13133214 | C4 | semidirect |
| 8. #16811013 | C4 | semidirect |
| 13. C4×#11719917 | C4 | semidirect |
| 15. #16810420 | C22 | semidirect |
| 18. C53×#354 | C22 | semidirect |
| 153. #2126 | D53 | semidirect |
| 174. #354 | C2×D53 | semidirect |
| 176. C53 | #13579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285168 | 2 |
| #20276400 | 2 |
| #20272871 | 2 |
| C53×#2126 | 2 |
| #13579 | 53 |