Finite Group DatabasebetaFinite Group DatabasebetaOrder 1701.
480 conjugacy classes of subgroups.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C7×3−1+2 | C3 | semidirect |
| 3. C3×#4430 | C3 | semidirect |
| 4. C32×C7⋊C9 | C3 | semidirect |
| 5. #10588065 | C3 | direct (N × H) |
| 6. C3×#4428 | C3 | semidirect |
| 7. C3×#4427 | C3 | semidirect |
| 8. C3×C9×ΓL(1,𝔽8) | C3 | semidirect |
| 12. C7×3−1+2 | C32 | semidirect |
| 15. #4430 | C32 | semidirect |
| 20. C3×C7⋊C9 | C32 | semidirect |
| 21. #4428 | C32 | semidirect |
| 22. #4427 | C32 | semidirect |
| 23. C9×ΓL(1,𝔽8) | C32 | semidirect |
| 28. C3×3−1+2 | ΓL(1,𝔽8) | semidirect |
| 47. 3−1+2 | C3×ΓL(1,𝔽8) | semidirect |
| 57. C3×C7 | #737 | semidirect |
| 70. C7 | C3×#737 | semidirect |
| 73. C3 | #10588065 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C7×3−1+2 | 3 |
| C3×C7⋊H(3,𝔽3) | 3 |
| C3×#4430 | 3 |
| C32×C7⋊C9 | 3 |
| #10588065 | 3 |
| C3×#4428 | 3 |
| C3×#4427 | 3 |
| C3×C9×ΓL(1,𝔽8) | 3 |
| C3×#737 | 7 |