Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
626 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 150 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 |
|---|---|---|
| 4. #16811568 | C4 | semidirect |
| 10. #16811559 | C4 | semidirect |
| 14. C2×C4⋊#88322 | C4 | semidirect |
| 16. C2×C8×Dic53 | C4 | semidirect |
| 17. C2×C4⋊C8×C53 | C4 | semidirect |
| 144. C2×C4⋊C8 | #6157 | semidirect |
| 154. C53 | #7980 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291162 | 2 |
| #20289578 | 2 |
| C2×#16810675 | 2 |
| #7980 | 53 |