Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
426 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C43 | C32⋊H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C43 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C43 ◁ C33×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×3−1+4 | C3 | semidirect |
| 2. C43×#6911 | C3 | semidirect |
| 3. C43×#6911 | C3 | semidirect |
| 4. C43×#6910 | C3 | semidirect |
| 5. C43×#6909 | C3 | semidirect |
| 6. C43×#6909 | C3 | semidirect |
| 7. C3×C43×#732 | C3 | semidirect |
| 8. C3×C43×#731 | C3 | semidirect |
| 9. C43×#6893 | C3 | semidirect |
| 64. #10624753 | C43 | direct (N × H) |
| 82. 3−1+4 | C3×C43 | semidirect |
| 83. #6911 | C3×C43 | semidirect |
| 84. #6911 | C3×C43 | semidirect |
| 85. #6910 | C3×C43 | semidirect |
| 86. #6909 | C3×C43 | semidirect |
| 87. #6909 | C3×C43 | semidirect |
| 88. C3×#732 | C3×C43 | semidirect |
| 89. C3×#731 | C3×C43 | semidirect |
| 90. #6893 | C3×C43 | semidirect |
| 119. C43 | #10624753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×3−1+4 | 3 |
| C43×#6911 | 3 |
| C43×#6910 | 3 |
| C43×#6909 | 3 |
| C3×C43×#732 | 3 |
| C3×C43×#731 | 3 |
| C43×#6893 | 3 |
| #10624753 | 43 |