Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
218 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 74 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×C43 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C43 |
| prime radical | C43×#6856 | C3 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C43 ◁ C32×C9×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#6894 | C3 | semidirect |
| 2. C43×#6893 | C3 | semidirect |
| 3. C9×3−1+2×C43 | C3 | semidirect |
| 4. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 5. C43×#6860 | C3 | semidirect |
| 6. C43×#6860 | C3 | semidirect |
| 7. C43×#6859 | C3 | semidirect |
| 8. C43×#6858 | C3 | semidirect |
| 9. C43×#6858 | C3 | semidirect |
| 10. C43×#6857 | C3 | semidirect |
| 11. C43×#6857 | C3 | semidirect |
| 12. C43×#6857 | C3 | semidirect |
| 63. #10624623 | C43 | direct (N × H) |
| 90. #6894 | C3×C43 | semidirect |
| 91. #6893 | C3×C43 | semidirect |
| 92. C9×3−1+2 | C3×C43 | semidirect |
| 93. C9×H(3,𝔽3) | C3×C43 | semidirect |
| 94. #6860 | C3×C43 | semidirect |
| 95. #6860 | C3×C43 | semidirect |
| 96. #6859 | C3×C43 | semidirect |
| 97. #6858 | C3×C43 | semidirect |
| 98. #6858 | C3×C43 | semidirect |
| 99. #6857 | C3×C43 | semidirect |
| 100. #6857 | C3×C43 | semidirect |
| 101. #6857 | C3×C43 | semidirect |
| 135. C43 | #10624623 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#6894 | 3 |
| C43×#6893 | 3 |
| C9×3−1+2×C43 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| C43×#6860 | 3 |
| C43×#6859 | 3 |
| C43×#6858 | 3 |
| C43×#6857 | 3 |
| C43×#6856 | 3 |
| #10624623 | 43 |