Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
608 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 142 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 |
|---|---|---|
| 191. C53 | #11235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#430 | 2 |
| #20290423 | 2 |
| D53⋊#338 | 2 |
| C2×#16811492 | 2 |
| #20283276 | 2 |
| #11235 | 53 |