Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
200 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 68 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 | #6911 |
| commutator, Frattini, cosocle | C3×C9 | C33×C43 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C43 ◁ C32×C43 ◁ C3×3−1+2×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C43×#6913 | C3 | semidirect |
| 2. C43×#6911 | C3 | semidirect |
| 3. C43×#6900 | C3 | semidirect |
| 4. C43×#6883 | C3 | semidirect |
| 5. C43×#6881 | C3 | semidirect |
| 6. C43×#6879 | C3 | semidirect |
| 7. C43×#6878 | C3 | semidirect |
| 12. C43×#733 | C32 | semidirect |
| 16. C43×#732 | C32 | semidirect |
| 20. C43×C9⋊C9 | C32 | semidirect |
| 21. C92×C43 | C32 | semidirect |
| 37. #10624851 | C43 | direct (N × H) |
| 50. #6913 | C3×C43 | semidirect |
| 51. #6911 | C3×C43 | semidirect |
| 52. #6900 | C3×C43 | semidirect |
| 53. #6883 | C3×C43 | semidirect |
| 54. #6881 | C3×C43 | semidirect |
| 55. #6879 | C3×C43 | semidirect |
| 56. #6878 | C3×C43 | semidirect |
| 67. #733 | C32×C43 | semidirect |
| 71. #732 | C32×C43 | semidirect |
| 75. C9⋊C9 | C32×C43 | semidirect |
| 76. C92 | C32×C43 | semidirect |
| 77. C43 | #10624851 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C43×#6913 | 3 |
| C43×#6911 | 3 |
| C43×#6900 | 3 |
| C43×#6883 | 3 |
| C43×#6881 | 3 |
| C43×#6879 | 3 |
| C43×#6878 | 3 |
| #10624851 | 43 |