Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
252 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 79 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×#13133157 | C4 | semidirect |
| 5. C22×#11719908 | C4 | semidirect |
| 10. #16810380 | C4 | semidirect |
| 14. C53×H(3,ℤ/4) | C4 | semidirect |
| 125. H(3,ℤ/4) | Dic53 | semidirect |
| 126. C53 | #7228 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276329 | 2 |
| #20274761 | 2 |
| C53×#1812 | 2 |
| #7228 | 53 |