Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
470 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20274744 | C2 | semidirect |
| 3. #20272725 | C2 | semidirect |
| 4. C2×C53×C22⋊C16 | C2 | semidirect |
| 5. C22×D424 | C4 | semidirect |
| 9. #16810859 | C4 | semidirect |
| 12. C2×#13133151 | C4 | semidirect |
| 15. #16810386 | C22 | semidirect |
| 19. C53×C22⋊C16 | C22 | semidirect |
| 154. C2×C22⋊C16 | D53 | semidirect |
| 178. C22⋊C16 | C2×D53 | semidirect |
| 180. C53 | #11886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810859 | 2 |
| #20274744 | 2 |
| #20272725 | 2 |
| C2×C53×C22⋊C16 | 2 |
| #11886 | 53 |