Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
232 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 232 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, socle | C32×C43 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C43 |
| 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×C9⋊H(3,𝔽3) | C3 | semidirect |
| 2. C9×H(3,𝔽3)×C43 | C3 | semidirect |
| 3. C43×#6887 | C3 | semidirect |
| 4. C43×#6861 | C3 | semidirect |
| 5. C43×#6861 | C3 | semidirect |
| 6. C43×#6859 | C3 | semidirect |
| 7. C43×#6859 | C3 | semidirect |
| 8. C43×#6856 | C3 | semidirect |
| 9. C43×#6856 | C3 | semidirect |
| 45. #10624601 | C43 | direct (N × H) |
| 66. C9⋊H(3,𝔽3) | C3×C43 | semidirect |
| 67. C9×H(3,𝔽3) | C3×C43 | semidirect |
| 68. #6887 | C3×C43 | semidirect |
| 69. #6861 | C3×C43 | semidirect |
| 70. #6861 | C3×C43 | semidirect |
| 71. #6859 | C3×C43 | semidirect |
| 72. #6859 | C3×C43 | semidirect |
| 73. #6856 | C3×C43 | semidirect |
| 74. #6856 | C3×C43 | semidirect |
| 99. C43 | #10624601 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×C9⋊H(3,𝔽3) | 3 |
| C9×H(3,𝔽3)×C43 | 3 |
| C43×#6887 | 3 |
| C43×#6861 | 3 |
| C43×#6859 | 3 |
| C43×#6856 | 3 |
| #10624601 | 43 |