Finite Group DatabasebetaFinite Group DatabasebetaOrder 34263.
386 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 386 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×C47 | C3×H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C47 |
| prime radical | C47×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C47 ◁ C34×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×3−1+2×C47 | C3 | semidirect |
| 2. C47×#6891 | C3 | semidirect |
| 3. C47×#6891 | C3 | semidirect |
| 5. C47×#6857 | C3 | semidirect |
| 46. #10624629 | C47 | direct (N × H) |
| 72. C32×3−1+2 | C3×C47 | semidirect |
| 73. #6891 | C3×C47 | semidirect |
| 74. #6891 | C3×C47 | semidirect |
| 76. #6857 | C3×C47 | semidirect |
| 104. C47 | #10624629 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×3−1+2×C47 | 3 |
| C47×#6891 | 3 |
| C47×C32⋊H(3,𝔽3) | 3 |
| C47×#6857 | 3 |
| #10624629 | 47 |