Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
334 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C43 | H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C43 |
| socle | C32×C43 | C3×H(3,𝔽3) |
| prime radical | C43×#6856 | C3 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C3×C9×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. C9×3−1+2×C43 | C3 | semidirect |
| 3. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 4. C43×#6860 | C3 | semidirect |
| 5. C43×#6859 | C3 | semidirect |
| 6. C43×#6858 | C3 | semidirect |
| 7. C43×#6857 | C3 | semidirect |
| 8. C43×#6857 | C3 | semidirect |
| 45. #10624583 | C43 | direct (N × H) |
| 64. C3×#737 | C3×C43 | semidirect |
| 65. C9×3−1+2 | C3×C43 | semidirect |
| 66. C9×H(3,𝔽3) | C3×C43 | semidirect |
| 67. #6860 | C3×C43 | semidirect |
| 68. #6859 | C3×C43 | semidirect |
| 69. #6858 | C3×C43 | semidirect |
| 70. #6857 | C3×C43 | semidirect |
| 71. #6857 | C3×C43 | semidirect |
| 95. C43 | #10624583 | 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 |
| 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 |
| #10624583 | 43 |