Finite Group DatabasebetaFinite Group DatabasebetaOrder 1701.
120 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 3. C7×C9⋊C9 | C3 | semidirect |
| 6. (C7⋊C9)⋊C9 | C3 | semidirect |
| 7. (C7⋊C9)⋊C9 | C3 | semidirect |
| 8. (C7⋊C9)⋊C9 | C3 | semidirect |
| 9. (C7⋊C9)⋊C9 | C3 | semidirect |
| 10. (C7⋊C9)⋊C9 | C3 | semidirect |
| 11. (C7⋊C9)⋊C9 | C3 | semidirect |
| 12. (C7⋊C9)⋊C9 | C3 | semidirect |
| 13. C9×C7⋊C9 | C3 | semidirect |
| 39. C9⋊C9 | ΓL(1,𝔽8) | semidirect |
| 58. C7⋊C9 | 3−1+2 | semidirect |
| 59. C7⋊C9 | 3−1+2 | semidirect |
| 97. C7 | #6896 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4428 | 3 |
| C3×#4427 | 3 |
| C7×C9⋊C9 | 3 |
| (C3×ΓL(1,𝔽8))⋊C9 | 3 |
| (C7⋊C9)⋊C9 | 3 |
| C9×C7⋊C9 | 3 |
| #6896 | 7 |