Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
342 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 1. C2×D53⋊C32 | C2 | semidirect |
| 2. #20289829 | C2 | semidirect |
| 3. C22⋊#13133267 | C2 | semidirect |
| 6. C2×#13133267 | C22 | semidirect |
| 64. C22×D53 | C32 | semidirect |
| 88. C22×C53 | C2×C32 | semidirect |
| 95. C2×D53 | C2×C32 | semidirect |
| 111. D53 | C22⋊C32 | semidirect |
| 122. C53 | C2×C22⋊C32 | semidirect |
| 202. C22 | D53⋊C32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D53⋊C32 | 2 |
| #20289829 | 2 |
| C22⋊#13133267 | 2 |
| C22×C16×D53 | 2 |
| C2×C22⋊C32 | 53 |