Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
182 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 3. #20272921 | C2 | semidirect |
| 12. C53×M64 | C4 | semidirect |
| 14. C2×C32×C53 | C4 | semidirect |
| 80. M64 | Dic53 | semidirect |
| 82. C2×C32 | Dic53 | semidirect |
| 87. C53 | #13638 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810453 | 2 |
| #20276499 | 2 |
| #20272921 | 2 |
| C2×C53×M64 | 2 |
| #13638 | 53 |