Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
498 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 123 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×C22⋊#11719908 | C2 | semidirect |
| 3. #20272729 | C2 | direct (N × H) |
| 4. C2×C53×#341 | C2 | semidirect |
| 15. C22⋊#11719908 | C22 | semidirect |
| 19. C53×#341 | C22 | semidirect |
| 149. C2×#341 | D53 | semidirect |
| 153. C2×C53 | #1349 | semidirect |
| 172. #341 | C2×D53 | semidirect |
| 173. C53 | C2×#1349 | semidirect |
| 303. C2 | #20272729 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810859 | 2 |
| C2×C22⋊#11719908 | 2 |
| #20272729 | 2 |
| C2×C53×#341 | 2 |
| C2×#1349 | 53 |