Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1566 conjugacy classes of subgroups; only the 563 normal subgroups are shown.
This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 563 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 |
|---|---|---|
| 9. #16810491 | C4 | semidirect |
| 12. C42×Dic53 | C4 | semidirect |
| 14. C53×#383 | C4 | semidirect |
| 50. C42×C53 | C42 | semidirect |
| 88. Dic53 | #383 | direct (N × H) |
| 104. #383 | Dic53 | direct (N × H) |
| 109. C53 | C4×#383 | semidirect |
| 147. C42 | C4×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810491 | 2 |
| C2×C42×Dic53 | 2 |
| #20272940 | 2 |
| #95×Dic53 | 2 |
| C2×C53×#383 | 2 |
| C4×#383 | 53 |