Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
204 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 204 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 | C3×H(3,𝔽3)×C43 | C32 |
| 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×#6895 | C3 | semidirect |
| 2. C43×#6894 | C3 | semidirect |
| 3. C9×3−1+2×C43 | C3 | semidirect |
| 5. C43×#6862 | C3 | semidirect |
| 6. C43×#6861 | C3 | semidirect |
| 9. C43×#6858 | C3 | semidirect |
| 10. C43×#6858 | C3 | semidirect |
| 11. C43×#6858 | C3 | semidirect |
| 12. C43×#6858 | C3 | semidirect |
| 60. #10624624 | C43 | direct (N × H) |
| 84. #6895 | C3×C43 | semidirect |
| 85. #6894 | C3×C43 | semidirect |
| 86. C9×3−1+2 | C3×C43 | semidirect |
| 88. #6862 | C3×C43 | semidirect |
| 89. #6861 | C3×C43 | semidirect |
| 92. #6858 | C3×C43 | semidirect |
| 93. #6858 | C3×C43 | semidirect |
| 94. #6858 | C3×C43 | semidirect |
| 95. #6858 | C3×C43 | semidirect |
| 128. C43 | #10624624 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#6895 | 3 |
| C43×#6894 | 3 |
| C9×3−1+2×C43 | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| C43×#6862 | 3 |
| C43×#6861 | 3 |
| C43×#6859 | 3 |
| C43×#6858 | 3 |
| C43×#6857 | 3 |
| #10624624 | 43 |