Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1030 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1030 conjugacy classes of subgroups — too many to draw. Only its 251 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×#16810997 | C2 | semidirect |
| 3. C2×#16810971 | C2 | semidirect |
| 4. #20274344 | C2 | direct (N × H) |
| 5. C2×#16810344 | C2 | semidirect |
| 6. C2×C53×#498 | C2 | semidirect |
| 14. #16810997 | C22 | semidirect |
| 16. #16810971 | C22 | semidirect |
| 19. #16810344 | C22 | semidirect |
| 22. C53×#498 | C22 | semidirect |
| 75. C2×C8×C53 | SD16 | semidirect |
| 113. C8×C53 | C2×SD16 | semidirect |
| 130. C2×#498 | D53 | semidirect |
| 136. C2×C53 | #1715 | semidirect |
| 147. #498 | C2×D53 | semidirect |
| 159. C53 | C2×#1715 | semidirect |
| 214. C2×C8 | #11719924 | semidirect |
| 249. C8 | C2×#11719924 | semidirect |
| 266. C2 | #20274344 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811000 | 2 |
| C2×#16810997 | 2 |
| C2×#16810971 | 2 |
| #20274344 | 2 |
| C2×#16810344 | 2 |
| C2×C53×#498 | 2 |
| C2×#1715 | 53 |