Finite Group DatabasebetaFinite Group DatabasebetaOrder 1701.
100 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×ΓL(1,𝔽8) |
| commutator, socle, cosocle | C32×C7 | C33 |
| Fitting | C7×C32⋊C9 | C3 |
| prime radical | C33×C7 | C32 |
| hypercenter | C32⋊C9 | ΓL(1,𝔽8) |
| hypocenter | C7 | #6897 |
| LCS | G ▷ C32×C7 ▷ C7 | |
| UCS | C1 ◁ C32 ◁ C32⋊C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #10588036 | C3 | semidirect |
| 6. #10588035 | 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 |
| 93. C7 | #6897 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×C32⋊C9 | 3 |
| C32⋊(C7⋊C9) | 3 |
| #10588036 | 3 |
| #10588035 | 3 |
| (C7⋊C9)⋊C9 | 3 |
| C9×C7⋊C9 | 3 |
| #6897 | 7 |