Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
450 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 3. #20272654 | C2 | semidirect |
| 112. C2×Dic53 | M32 | semidirect |
| 162. C53 | #11440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133146 | 2 |
| #20276326 | 2 |
| #20272654 | 2 |
| C53×#2112 | 2 |
| #11440 | 53 |