Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
604 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 604 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 |
|---|---|---|
| 2. C2×#16810672 | C2 | semidirect |
| 3. #20276930 | C2 | direct (N × H) |
| 4. C2×#16810446 | C2 | semidirect |
| 5. C2×#16810437 | C2 | semidirect |
| 6. C2×C53×#349 | C2 | semidirect |
| 13. #16810672 | C22 | semidirect |
| 18. #16810446 | C22 | semidirect |
| 19. #16810437 | C22 | semidirect |
| 22. C53×#349 | C22 | semidirect |
| 152. C2×#349 | D53 | semidirect |
| 156. C2×C53 | #2238 | semidirect |
| 174. #349 | C2×D53 | semidirect |
| 175. C53 | C2×#2238 | semidirect |
| 303. C2 | #20276930 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810876 | 2 |
| C2×#16810672 | 2 |
| #20276930 | 2 |
| C2×#16810446 | 2 |
| C2×#16810437 | 2 |
| C2×C53×#349 | 2 |
| C2×#2238 | 53 |