Finite Group DatabasebetaFinite Group DatabasebetaOrder 34263.
446 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 92 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×C47 | C32⋊H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C33×C47 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C47 ◁ C33×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×#6912 | C3 | semidirect |
| 3. C47×#6910 | C3 | semidirect |
| 4. C47×#6909 | C3 | semidirect |
| 5. C3×C47×AΣL(1,𝔽27) | C3 | semidirect |
| 41. #10624755 | C47 | direct (N × H) |
| 55. C32×3−1+2 | C3×C47 | semidirect |
| 56. #6912 | C3×C47 | semidirect |
| 57. #6910 | C3×C47 | semidirect |
| 58. #6909 | C3×C47 | semidirect |
| 59. C3×AΣL(1,𝔽27) | C3×C47 | semidirect |
| 79. C47 | #10624755 | 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×#6912 | 3 |
| C47×#6910 | 3 |
| C47×#6909 | 3 |
| C3×C47×AΣL(1,𝔽27) | 3 |
| #10624755 | 47 |