Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1138 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1138 conjugacy classes of subgroups — too many to draw. Only its 187 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×#16811013 | C2 | semidirect |
| 2. C2×#16810989 | C2 | semidirect |
| 3. #20274008 | C2 | direct (N × H) |
| 4. C2×#16810365 | C2 | semidirect |
| 5. C2×#16810363 | C2 | semidirect |
| 6. C2×C53×#562 | C2 | semidirect |
| 11. #16811013 | C22 | semidirect |
| 13. #16810989 | C22 | semidirect |
| 17. #16810365 | C22 | semidirect |
| 18. #16810363 | C22 | semidirect |
| 21. C53×#562 | C22 | semidirect |
| 157. C2×#562 | D53 | semidirect |
| 164. C2×C53 | #1656 | semidirect |
| 172. #562 | C2×D53 | semidirect |
| 188. C53 | C2×#1656 | semidirect |
| 320. C2 | #20274008 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811013 | 2 |
| C2×#16810989 | 2 |
| #20274008 | 2 |
| C2×#16810365 | 2 |
| C2×#16810363 | 2 |
| C2×C53×#562 | 2 |
| C2×#1656 | 53 |