Finite Group DatabasebetaFinite Group DatabasebetaOrder 5103.
932 conjugacy classes of subgroups; only the 548 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 548 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C7 | C33 |
| commutator, Frattini | C32 | C34×C7 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C33×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C7×#6894 | C3 | direct (N × H) |
| 4. C3×C7×C9⋊C9 | C3 | semidirect |
| 5. C3×C7×C9⋊C9 | C3 | semidirect |
| 7. C3×#6894 | C7 | direct (N × H) |
| 17. C7×C9⋊C9 | C32 | semidirect |
| 18. C7×C9⋊C9 | C32 | semidirect |
| 22. #6894 | C3×C7 | direct (N × H) |
| 23. C3×C9⋊C9 | C3×C7 | semidirect |
| 24. C3×C9⋊C9 | C3×C7 | semidirect |
| 36. C3×C7×C9 | 3−1+2 | semidirect |
| 50. C9⋊C9 | C32×C7 | semidirect |
| 51. C9⋊C9 | C32×C7 | semidirect |
| 64. C7×C9 | C3×3−1+2 | semidirect |
| 75. C3×C9 | C7×3−1+2 | semidirect |
| 81. C3×C7 | #6894 | direct (N × H) |
| 96. C9 | C3×C7×3−1+2 | semidirect |
| 97. C7 | C3×#6894 | direct (N × H) |
| 99. C3 | C7×#6894 | direct (N × H) |