Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1138 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1138 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×#16811371 | C2 | semidirect |
| 2. C2×#16811010 | C2 | semidirect |
| 3. #20274007 | C2 | direct (N × H) |
| 4. C2×#16810365 | C2 | semidirect |
| 5. C2×#16810362 | C2 | semidirect |
| 6. C2×C53×#490 | C2 | semidirect |
| 11. #16811371 | C22 | semidirect |
| 17. #16811010 | C22 | semidirect |
| 19. #16810365 | C22 | semidirect |
| 20. #16810362 | C22 | semidirect |
| 24. C53×#490 | C22 | semidirect |
| 159. C2×#490 | D53 | semidirect |
| 164. C2×C53 | #1656 | semidirect |
| 182. #490 | C2×D53 | semidirect |
| 188. C53 | C2×#1656 | semidirect |
| 320. C2 | #20274007 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811371 | 2 |
| C2×#16811010 | 2 |
| #20274007 | 2 |
| C2×#16810365 | 2 |
| C2×#16810362 | 2 |
| C2×C53×#490 | 2 |
| C2×#1656 | 53 |