Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
730 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 730 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 |
|---|---|---|
| 5. C2×C22⋊#88322 | C4 | semidirect |
| 24. C2×C22⋊C4×C53 | C8 | semidirect |
| 153. C53 | #7032 | semidirect |
| 166. C2×C22⋊C4 | #88322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274625 | 2 |
| C53×C22⋊#95 | 2 |
| #7032 | 53 |