Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
252 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 56 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 |
|---|---|---|
| 4. C2×#13133292 | C4 | semidirect |
| 5. C2×D53⋊C16 | C4 | semidirect |
| 10. #16811491 | C4 | semidirect |
| 14. #16810380 | C4 | semidirect |
| 15. C53×H(3,ℤ/4) | C4 | semidirect |
| 133. H(3,ℤ/4) | #6157 | semidirect |
| 134. C53 | #7228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290946 | 2 |
| #20290598 | 2 |
| #20274760 | 2 |
| #7228 | 53 |