Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
682 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 682 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 |
|---|---|---|
| 3. #20276820 | C2 | direct (N × H) |
| 4. C2×#16810451 | C2 | semidirect |
| 5. C2×#16810427 | C2 | semidirect |
| 6. C22×Q32×C53 | C2 | semidirect |
| 16. #16810451 | C22 | semidirect |
| 17. #16810427 | C22 | semidirect |
| 20. C2×Q32×C53 | C22 | semidirect |
| 116. C22×Q32 | D53 | semidirect |
| 122. C2×C53 | #2219 | semidirect |
| 130. C2×Q32 | C2×D53 | semidirect |
| 141. C53 | C2×#2219 | semidirect |
| 236. C2 | #20276820 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133156 | 2 |
| C2×#16810861 | 2 |
| #20276820 | 2 |
| C2×#16810451 | 2 |
| C2×#16810427 | 2 |
| C22×Q32×C53 | 2 |
| C2×#2219 | 53 |