Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 5. #16811468 | C4 | semidirect |
| 23. C2×C4×Dic53 | C8 | semidirect |
| 30. C2×C4⋊C4×C53 | C8 | semidirect |
| 169. C53 | #7189 | semidirect |
| 183. C2×C4⋊C4 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811468 | 2 |
| #20272944 | 2 |
| #7189 | 53 |