Finite Group DatabasebetaFinite Group DatabasebetaOrder 34263.
458 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 104 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 | C34×C47 | C32 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C47 ◁ C34×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×C47×#733 | C3 | semidirect |
| 32. #10624744 | C47 | direct (N × H) |
| 41. C32×C47 | #733 | semidirect |
| 48. C3×#733 | C3×C47 | semidirect |
| 69. C47 | #10624744 | direct (N × H) |
| 93. C32 | C47×#733 | semidirect |
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 |
| C3×C47×#733 | 3 |
| C47×#6891 | 3 |
| C3×C47×C32⋊C9 | 3 |
| #10624744 | 47 |