Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
150 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 45 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. #20272809 | C2 | semidirect |
| 3. C53×C22⋊C32 | C2 | semidirect |
| 67. C22⋊C32 | D53 | semidirect |
| 81. C53 | #7420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276801 | 2 |
| #20272809 | 2 |
| C53×C22⋊C32 | 2 |
| #7420 | 53 |