Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1074 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1074 conjugacy classes of subgroups — too many to draw. Only its 203 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×#16811002 | C2 | semidirect |
| 3. C2×#16810914 | C2 | semidirect |
| 4. #20273861 | C2 | direct (N × H) |
| 5. C2×#16810350 | C2 | semidirect |
| 6. C2×C53×#333 | C2 | semidirect |
| 17. #16811002 | C22 | semidirect |
| 19. #16810914 | C22 | semidirect |
| 23. #16810350 | C22 | semidirect |
| 26. C53×#333 | C22 | semidirect |
| 156. C2×#333 | D53 | semidirect |
| 158. C2×C53 | #1634 | semidirect |
| 180. #333 | C2×D53 | semidirect |
| 182. C53 | C2×#1634 | semidirect |
| 308. C2 | #20273861 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16811339 | 2 |
| C2×#16811002 | 2 |
| C2×#16810914 | 2 |
| #20273861 | 2 |
| C2×#16810350 | 2 |
| C2×C53×#333 | 2 |
| C2×#1634 | 53 |