Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
2774 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 2774 conjugacy classes of subgroups — too many to draw. Only its 291 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. C22×#13133134 | C2 | semidirect |
| 3. C2×#16810409 | C2 | direct (N × H) |
| 4. C22×#99×C53 | C2 | semidirect |
| 5. C25×D53 | C4 | semidirect |
| 10. C2×#13133185 | C4 | semidirect |
| 12. C22×C22⋊Dic53 | C4 | semidirect |
| 15. C2×#13133134 | C22 | semidirect |
| 16. #16810409 | C22 | direct (N × H) |
| 20. C2×#99×C53 | C22 | semidirect |
| 26. C24×D53 | C2×C4 | semidirect |
| 37. #13133185 | C2×C4 | semidirect |
| 40. C2×C22⋊Dic53 | C2×C4 | semidirect |
| 44. #13133134 | C23 | semidirect |
| 58. #99×C53 | C23 | semidirect |
| 85. C23×D53 | C22×C4 | semidirect |
| 114. C22⋊Dic53 | C22×C4 | semidirect |
| 197. C22×C53 | AΣL(1,𝔽16) | semidirect |
| 215. C22×#99 | D53 | semidirect |
| 223. C2×C53 | C2×AΣL(1,𝔽16) | semidirect |
| 240. C2×#99 | C2×D53 | semidirect |
| 242. C53 | C22×AΣL(1,𝔽16) | semidirect |
| 280. #99 | C22×D53 | semidirect |
| 426. C22 | #16810409 | direct (N × H) |
| 441. C2 | C2×#16810409 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13133185 | 2 |
| C22×#13133134 | 2 |
| C2×#16810409 | 2 |
| C22×#99×C53 | 2 |
| C22×AΣL(1,𝔽16) | 53 |