Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 2. C2×#16811544 | C2 | semidirect |
| 4. #20289754 | C2 | semidirect |
| 54. C22⋊Dic53 | C16 | semidirect |
| 89. C2×Dic53 | C2×C16 | semidirect |
| 100. C22×C53 | C4⋊C16 | semidirect |
| 135. C53 | #12912 | semidirect |
| 217. C22 | #16811544 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11719910 | 2 |
| C2×#16811544 | 2 |
| C2×C22⋊#11719910 | 2 |
| #20289754 | 2 |
| #20274489 | 2 |
| #12912 | 53 |