Finite Group DatabasebetaFinite Group DatabasebetaOrder 31347.
374 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 134 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C33×C43 | C33 |
| commutator, Frattini, cosocle | C33 | C33×C43 |
| prime radical | C34×C43 | C32 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C33×C43 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C43×C9⋊C9 | C3 | semidirect |
| 2. C3×C43×C9⋊C9 | C3 | semidirect |
| 6. C43×#6855 | C3 | semidirect |
| 7. C43×#6855 | C3 | semidirect |
| 8. C43×#6855 | C3 | semidirect |
| 9. C43×#6855 | C3 | semidirect |
| 63. #10624566 | C43 | direct (N × H) |
| 90. C3×C9⋊C9 | C3×C43 | semidirect |
| 91. C3×C9⋊C9 | C3×C43 | semidirect |
| 95. #6855 | C3×C43 | semidirect |
| 96. #6855 | C3×C43 | semidirect |
| 97. #6855 | C3×C43 | semidirect |
| 98. #6855 | C3×C43 | semidirect |
| 123. C43 | #10624566 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C43×C9⋊C9 | 3 |
| C3×C43×C32⋊C9 | 3 |
| C43×#6855 | 3 |
| #10624566 | 43 |