Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
438 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
| 88. C2×Dic53 | M32 | semidirect |
| 134. C53 | #12913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133291 | 2 |
| C2×#16811544 | 2 |
| C2×C22⋊#11719910 | 2 |
| #20289754 | 2 |
| #20274489 | 2 |
| #12913 | 53 |