Finite Group DatabasebetaFinite Group DatabasebetaOrder 34263.
184 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 74 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 | C3×H(3,𝔽3)×C47 | C32 |
| LCS | G ▷ C33 ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C47 ◁ C32×C9×C47 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C47×#6895 | C3 | semidirect |
| 2. C47×#6894 | C3 | semidirect |
| 4. C47×#6862 | C3 | semidirect |
| 5. C47×#6861 | C3 | semidirect |
| 7. C47×#6858 | C3 | semidirect |
| 8. C47×#6858 | C3 | semidirect |
| 40. #10624676 | C47 | direct (N × H) |
| 57. #6895 | C3×C47 | semidirect |
| 58. #6894 | C3×C47 | semidirect |
| 60. #6862 | C3×C47 | semidirect |
| 61. #6861 | C3×C47 | semidirect |
| 63. #6858 | C3×C47 | semidirect |
| 64. #6858 | C3×C47 | semidirect |
| 86. C47 | #10624676 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C47×#6895 | 3 |
| C47×#6894 | 3 |
| C47×C9⋊H(3,𝔽3) | 3 |
| C47×#6862 | 3 |
| C47×#6861 | 3 |
| C47×#6859 | 3 |
| C47×#6858 | 3 |
| C47×#6857 | 3 |
| #10624676 | 47 |