Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
180 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4⋊#13133123 | C2 | semidirect |
| 5. #20272848 | C2 | semidirect |
| 6. C32×Dic53 | C2 | semidirect |
| 7. C53×C4⋊C32 | C2 | semidirect |
| 84. C4⋊C32 | D53 | semidirect |
| 104. C53 | #13641 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276310 | 2 |
| C4⋊#13133123 | 2 |
| #20272852 | 2 |
| #20272848 | 2 |
| C32×Dic53 | 2 |
| C53×C4⋊C32 | 2 |
| #13641 | 53 |