Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
858 conjugacy classes of subgroups; only the 268 normal subgroups are shown.
This group has 858 conjugacy classes of subgroups — too many to draw. Only its 268 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 | direct (N × H) |
| 101. C4×C53 | #338 | semidirect |
| 126. C53 | C4×#338 | semidirect |
| 213. C4 | #16811492 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D53⋊M16 | 2 |
| C2×#16811492 | 2 |
| C2×C4×#11719912 | 2 |
| C4×#338 | 53 |