Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
470 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
| LCS | G ▷ C33 ▷ C3 ▷ 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. C3×C43×#737 | C3 | semidirect |
| 2. C3×C43×#733 | C3 | semidirect |
| 3. C3×C43×#732 | C3 | semidirect |
| 4. C3×C43×#731 | C3 | semidirect |
| 5. C3×C43×#731 | C3 | semidirect |
| 6. C3×C43×AΣL(1,𝔽27) | C3 | semidirect |
| 7. C3×C43×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C43×#6893 | C3 | semidirect |
| 9. C3×C43×C32⋊C9 | C3 | semidirect |
| 70. #10624746 | C43 | direct (N × H) |
| 94. C3×#737 | C3×C43 | semidirect |
| 95. C3×#733 | C3×C43 | semidirect |
| 96. C3×#732 | C3×C43 | semidirect |
| 97. C3×#731 | C3×C43 | semidirect |
| 98. C3×#731 | C3×C43 | semidirect |
| 99. C3×AΣL(1,𝔽27) | C3×C43 | semidirect |
| 100. C3×AΣL(1,𝔽27) | C3×C43 | semidirect |
| 101. #6893 | C3×C43 | semidirect |
| 102. C3×C32⋊C9 | C3×C43 | semidirect |
| 134. C43 | #10624746 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C43×#737 | 3 |
| C3×C43×#733 | 3 |
| C3×C43×#732 | 3 |
| C3×C43×#731 | 3 |
| C3×C43×AΣL(1,𝔽27) | 3 |
| C43×#6893 | 3 |
| C3×C43×C32⋊C9 | 3 |
| #10624746 | 43 |