Finite Group DatabasebetaFinite Group DatabasebetaOrder 34263.
414 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 414 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. C3×C47×#737 | C3 | semidirect |
| 2. C47×#6912 | C3 | semidirect |
| 3. C47×#6911 | C3 | semidirect |
| 4. C47×#6910 | C3 | semidirect |
| 5. C47×#6910 | C3 | semidirect |
| 6. C47×#6909 | C3 | semidirect |
| 7. C47×#6909 | C3 | semidirect |
| 8. C3×C47×#731 | C3 | semidirect |
| 9. C3×C47×#731 | C3 | semidirect |
| 68. #10624756 | C47 | direct (N × H) |
| 86. C3×#737 | C3×C47 | semidirect |
| 87. #6912 | C3×C47 | semidirect |
| 88. #6911 | C3×C47 | semidirect |
| 89. #6910 | C3×C47 | semidirect |
| 90. #6910 | C3×C47 | semidirect |
| 91. #6909 | C3×C47 | semidirect |
| 92. #6909 | C3×C47 | semidirect |
| 93. C3×#731 | C3×C47 | semidirect |
| 94. C3×#731 | C3×C47 | semidirect |
| 125. C47 | #10624756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C47×#737 | 3 |
| C47×#6912 | 3 |
| C47×#6911 | 3 |
| C47×#6910 | 3 |
| C47×#6909 | 3 |
| C3×C47×#731 | 3 |
| #10624756 | 47 |