Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1434 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 275 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. #20275891 | C2 | direct (N × H) |
| 3. C2×#16810389 | C2 | semidirect |
| 4. C2×C53×#543 | C2 | semidirect |
| 10. #16810389 | C22 | semidirect |
| 12. C53×#543 | C22 | semidirect |
| 15. C24×D53 | Q8 | semidirect |
| 20. C22×C22⋊D53 | Q8 | semidirect |
| 23. C23×Dic53 | Q8 | semidirect |
| 54. C23×D53 | C2×Q8 | semidirect |
| 77. C22×Dic53 | C2×Q8 | semidirect |
| 157. C2×#543 | D53 | semidirect |
| 167. C2×C53 | #2032 | semidirect |
| 172. #543 | C2×D53 | semidirect |
| 180. C53 | C2×#2032 | semidirect |
| 329. C2 | #20275891 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133131 | 2 |
| #20275891 | 2 |
| C2×#16810389 | 2 |
| C2×C53×#543 | 2 |
| C2×#2032 | 53 |