Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16810405 | C2 | semidirect |
| 3. #20272699 | C2 | direct (N × H) |
| 4. C2×C53×H(3,ℤ/4) | C2 | semidirect |
| 5. C22×D424 | C4 | semidirect |
| 10. #16810876 | C4 | semidirect |
| 12. C2×#13133149 | C4 | semidirect |
| 15. #16810405 | C22 | semidirect |
| 19. C53×H(3,ℤ/4) | C22 | semidirect |
| 25. C2×D424 | C2×C4 | semidirect |
| 36. #13133149 | C2×C4 | semidirect |
| 172. C2×H(3,ℤ/4) | D53 | semidirect |
| 178. C2×C53 | #1339 | semidirect |
| 195. H(3,ℤ/4) | C2×D53 | semidirect |
| 196. C53 | C2×#1339 | semidirect |
| 351. C2 | #20272699 | 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 |
| C2×#16810405 | 2 |
| #20272699 | 2 |
| C2×C53×H(3,ℤ/4) | 2 |
| C2×#1339 | 53 |