Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
514 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 163 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×#16810428 | C2 | semidirect |
| 4. #20274879 | C2 | semidirect |
| 5. C2×C4×C16×C53 | C2 | semidirect |
| 11. #16811007 | C4 | semidirect |
| 132. C2×C4×C16 | D53 | semidirect |
| 153. C53 | #13204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811007 | 2 |
| C2×#16810428 | 2 |
| C2×#16810425 | 2 |
| #20274879 | 2 |
| C2×C4×C16×C53 | 2 |
| #13204 | 53 |