Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
858 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 858 conjugacy classes of subgroups — too many to draw. Only its 254 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. #16811492 | C4 | semidirect |
| 11. #16810381 | C4 | semidirect |
| 12. C53×#338 | C4 | semidirect |
| 85. #6157 | #338 | direct (N × H) |
| 105. #338 | #6157 | direct (N × H) |
| 106. C53 | C4×#338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×#6157 | 2 |
| D53⋊#338 | 2 |
| #338×D53 | 2 |
| C4×#338 | 53 |