Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 45. C2×Q16×C53 | C8 | semidirect |
| 148. C53 | #9658 | semidirect |
| 152. C2×Q16 | #88324 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290884 | 2 |
| C2×#16811484 | 2 |
| C2×Q8⋊#88324 | 2 |
| C2×#16811464 | 2 |
| C2×Q16×Dic53 | 2 |
| #9658 | 53 |