Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
152 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 6. C2×Q32×C53 | C4 | semidirect |
| 9. C53×#366 | C4 | semidirect |
| 75. C2×Q32 | Dic53 | semidirect |
| 80. #366 | Dic53 | semidirect |
| 82. C53 | #7419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊#13133123 | 2 |
| #20272807 | 2 |
| C53×#2216 | 2 |
| #7419 | 53 |