Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
554 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 554 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. C32×H(3,𝔽3)×C43 | C3 | semidirect |
| 2. C43×#6911 | C3 | semidirect |
| 3. C43×#6910 | C3 | semidirect |
| 4. C43×#6909 | C3 | semidirect |
| 5. C3×C43×AΣL(1,𝔽27) | C3 | semidirect |
| 8. C3×3−1+2×C43 | C32 | semidirect |
| 9. C3×3−1+2×C43 | C32 | semidirect |
| 13. C3×H(3,𝔽3)×C43 | C32 | semidirect |
| 39. #10624754 | C43 | direct (N × H) |
| 55. C32×H(3,𝔽3) | C3×C43 | semidirect |
| 56. #6911 | C3×C43 | semidirect |
| 57. #6910 | C3×C43 | semidirect |
| 58. #6909 | C3×C43 | semidirect |
| 59. C3×AΣL(1,𝔽27) | C3×C43 | semidirect |
| 69. C3×3−1+2 | C32×C43 | semidirect |
| 70. C3×3−1+2 | C32×C43 | semidirect |
| 74. C3×H(3,𝔽3) | C32×C43 | semidirect |
| 80. C43 | #10624754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×H(3,𝔽3)×C43 | 3 |
| C43×#6911 | 3 |
| C43×#6910 | 3 |
| C43×#6909 | 3 |
| C3×C43×AΣL(1,𝔽27) | 3 |
| #10624754 | 43 |