Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1426 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 1426 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
|---|---|---|
| 10. C22×C4⋊Dic53 | C4 | semidirect |
| 11. C22×#11719919 | C4 | semidirect |
| 13. C23×Q8×C53 | C4 | semidirect |
| 18. C2×C22⋊#6157 | Q8 | semidirect |
| 153. C23×Q8 | #6157 | semidirect |
| 163. C53 | #11381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811501 | 2 |
| #20289889 | 2 |
| C22×#13133193 | 2 |
| #11381 | 53 |