Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
866 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 866 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×#16810973 | C2 | semidirect |
| 4. #20274317 | C2 | direct (N × H) |
| 5. C2×C8×#88322 | C2 | semidirect |
| 6. C2×C53×#498 | C2 | semidirect |
| 13. #16810973 | C22 | semidirect |
| 19. C8×#88322 | C22 | semidirect |
| 22. C53×#498 | C22 | semidirect |
| 122. C2×#498 | D53 | semidirect |
| 128. C2×C53 | #1708 | semidirect |
| 137. #498 | C2×D53 | semidirect |
| 150. C53 | C2×#1708 | semidirect |
| 248. C2 | #20274317 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810996 | 2 |
| C2×#16810973 | 2 |
| C2×#16810971 | 2 |
| #20274317 | 2 |
| C2×C8×#88322 | 2 |
| C2×C53×#498 | 2 |
| C2×#1708 | 53 |