Finite Group DatabasebetaFinite Group DatabasebetaOrder 38637.
216 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 80 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×H(3,𝔽3)×C53 | C32 |
| 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 |
|---|---|---|
| 1. C53×#6895 | C3 | semidirect |
| 3. C53×#6887 | C3 | semidirect |
| 4. C3×C53×C9⋊C9 | C3 | semidirect |
| 5. C53×3−1+2⋊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. C53×3−1+2⋊C9 | C3 | semidirect |
| 57. #10624827 | C53 | direct (N × H) |
| 80. #6895 | C3×C53 | semidirect |
| 82. #6887 | C3×C53 | semidirect |
| 83. C3×C9⋊C9 | C3×C53 | semidirect |
| 84. 3−1+2⋊C9 | C3×C53 | semidirect |
| 85. 3−1+2⋊C9 | C3×C53 | semidirect |
| 86. 3−1+2⋊C9 | C3×C53 | semidirect |
| 87. 3−1+2⋊C9 | C3×C53 | semidirect |
| 88. 3−1+2⋊C9 | C3×C53 | semidirect |
| 89. 3−1+2⋊C9 | C3×C53 | semidirect |
| 120. C53 | #10624827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C53×#6895 | 3 |
| C53×#6893 | 3 |
| C53×#6887 | 3 |
| C3×C53×C9⋊C9 | 3 |
| C53×3−1+2⋊C9 | 3 |
| C53×H(3,𝔽3)⋊C9 | 3 |
| #10624827 | 53 |