Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1294 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1294 conjugacy classes of subgroups — too many to draw. Only its 216 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×#16811492 | C2 | semidirect |
| 146. C2×D53 | #338 | semidirect |
| 176. C53 | C22⋊#338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D53⋊#407 | 2 |
| C2×#16811492 | 2 |
| C22×M16×D53 | 2 |
| C22⋊#338 | 53 |