Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
194 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 115 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. #20272917 | C2 | semidirect |
| 4. #20272915 | C2 | semidirect |
| 14. C53×M64 | C4 | semidirect |
| 28. C32×C53 | C2×C4 | semidirect |
| 79. M64 | Dic53 | semidirect |
| 86. C53 | #13634 | semidirect |
| 99. C32 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276499 | 2 |
| C2×#16810449 | 2 |
| #20272917 | 2 |
| #20272915 | 2 |
| C2×C53×M64 | 2 |
| #13634 | 53 |