Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
882 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 882 conjugacy classes of subgroups — too many to draw. Only its 171 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×C53⋊#564 | C2 | semidirect |
| 3. #20274016 | C2 | direct (N × H) |
| 4. C2×#16810365 | C2 | semidirect |
| 5. C2×#16810364 | C2 | semidirect |
| 9. C53⋊#564 | C22 | semidirect |
| 19. #16810365 | C22 | semidirect |
| 20. #16810364 | C22 | semidirect |
| 143. C2×C53 | #1658 | semidirect |
| 166. C53 | C2×#1658 | semidirect |
| 276. C2 | #20274016 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C53⋊#564 | 2 |
| C2×#16810987 | 2 |
| #20274016 | 2 |
| C2×#16810365 | 2 |
| C2×#16810364 | 2 |
| C2×C53×#490 | 2 |
| C2×#1658 | 53 |