Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20276336 | C2 | semidirect |
| 3. #20272699 | C2 | semidirect |
| 4. C53×#1812 | C2 | semidirect |
| 5. C22×D424 | C4 | semidirect |
| 8. #16810876 | C4 | semidirect |
| 12. #16810661 | C4 | semidirect |
| 15. #16810405 | C22 | semidirect |
| 19. C53×H(3,ℤ/4) | C22 | semidirect |
| 147. #1812 | D53 | semidirect |
| 169. H(3,ℤ/4) | C2×D53 | semidirect |
| 170. C53 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20284363 | 2 |
| #20276336 | 2 |
| #20272699 | 2 |
| C53×#1812 | 2 |
| #11868 | 53 |