Finite Group DatabasebetaFinite Group DatabasebetaOrder 38637.
272 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C53 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C53 |
| prime radical | C3×C53×AΣL(1,𝔽27) | C3 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C53 ◁ C32×C9×C53 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C53×#6894 | C3 | semidirect |
| 3. C53×C9⋊H(3,𝔽3) | C3 | semidirect |
| 4. C9×3−1+2×C53 | C3 | semidirect |
| 5. C3×C53×C32⋊C9 | C3 | semidirect |
| 6. C53×3−1+2⋊C9 | C3 | semidirect |
| 7. C53×3−1+2⋊C9 | C3 | semidirect |
| 8. C53×3−1+2⋊C9 | C3 | semidirect |
| 9. C53×3−1+2⋊C9 | C3 | semidirect |
| 10. C53×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 11. C53×H(3,𝔽3)⋊C9 | C3 | semidirect |
| 12. C53×#6866 | C3 | semidirect |
| 13. C53×#6866 | C3 | semidirect |
| 52. 3−1+2×C53 | 3−1+2 | semidirect |
| 71. #10624801 | C53 | direct (N × H) |
| 102. #6894 | C3×C53 | semidirect |
| 103. C9⋊H(3,𝔽3) | C3×C53 | semidirect |
| 104. C9×3−1+2 | C3×C53 | semidirect |
| 105. C3×C32⋊C9 | C3×C53 | semidirect |
| 106. 3−1+2⋊C9 | C3×C53 | semidirect |
| 107. 3−1+2⋊C9 | C3×C53 | semidirect |
| 108. 3−1+2⋊C9 | C3×C53 | semidirect |
| 109. 3−1+2⋊C9 | C3×C53 | semidirect |
| 110. H(3,𝔽3)⋊C9 | C3×C53 | semidirect |
| 111. H(3,𝔽3)⋊C9 | C3×C53 | semidirect |
| 112. #6866 | C3×C53 | semidirect |
| 113. #6866 | C3×C53 | semidirect |
| 148. C53 | #10624801 | direct (N × H) |
| 161. 3−1+2 | 3−1+2×C53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C53×AΣL(1,𝔽27) | 3 |
| C53×#6894 | 3 |
| C53×C9⋊H(3,𝔽3) | 3 |
| C9×3−1+2×C53 | 3 |
| C3×C53×C32⋊C9 | 3 |
| C53×3−1+2⋊C9 | 3 |
| C53×H(3,𝔽3)⋊C9 | 3 |
| C53×#6866 | 3 |
| #10624801 | 53 |