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. #20276929 | C2 | direct (N × H) |
| 3. C2×#16810447 | C2 | semidirect |
| 4. C2×#16810435 | C2 | semidirect |
| 5. C2×#16810405 | C2 | semidirect |
| 6. C2×C53×#430 | C2 | semidirect |
| 14. #16810447 | C22 | semidirect |
| 15. #16810435 | C22 | semidirect |
| 16. #16810405 | C22 | semidirect |
| 20. C53×#430 | C22 | semidirect |
| 148. C2×#430 | D53 | semidirect |
| 156. C2×C53 | #2238 | semidirect |
| 167. #430 | C2×D53 | semidirect |
| 175. C53 | C2×#2238 | semidirect |
| 303. C2 | #20276929 | 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 |
| #20276929 | 2 |
| C2×#16810447 | 2 |
| C2×#16810435 | 2 |
| C2×#16810405 | 2 |
| C2×C53×#430 | 2 |
| C2×#2238 | 53 |