Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1566 conjugacy classes of subgroups; only the 635 normal subgroups are shown.
This group has 1566 conjugacy classes of subgroups — too many to draw. Only its 635 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 |
|---|---|---|
| 6. #16810491 | C4 | direct (N × H) |
| 12. C43×C53 | C4 | semidirect |
| 42. C42×C53 | C42 | semidirect |
| 70. C4×C53 | #383 | semidirect |
| 87. C43 | Dic53 | semidirect |
| 88. C53 | C4×#383 | semidirect |
| 119. C42 | C4×Dic53 | semidirect |
| 146. C4 | #16810491 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810491 | 2 |
| #20272942 | 2 |
| C4×#13133124 | 2 |
| C2×C43×C53 | 2 |
| C4×#383 | 53 |