Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
314 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 7. #16810453 | C4 | direct (N × H) |
| 61. C4×C53 | #368 | semidirect |
| 80. C53 | C4×#368 | semidirect |
| 128. C4 | #16810453 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810453 | 2 |
| C4×#13133153 | 2 |
| #20272809 | 2 |
| C2×C4×C16×C53 | 2 |
| C4×#368 | 53 |