Finite Group DatabasebetaFinite Group DatabasebetaOrder 33300.
192 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #16814881⋊C3 |
| commutator, hypocenter | C52×C37 | C32×C4 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C37 | C3×C4 |
| prime radical | C3×C5⋊(C5⋊(D37⋊C3)) | C2 |
| cosocle | C5⋊D185 | C2×C32 |
| LCS | G ▷ C52×C37 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#16814881 | C3 | semidirect |
| 3. #16814881⋊C3 | C3 | direct (N × H) |
| 4. C3×C52×C37⋊C3 | C4 | semidirect |
| 9. #16814881 | C32 | semidirect |
| 13. C52×C37⋊C3 | C3×C4 | semidirect |
| 14. C3×C52×C37 | C3×C4 | semidirect |
| 21. C3×C5×C37⋊C3 | AGL(1,𝔽5) | semidirect |
| 22. C3×C5×C37⋊C3 | AGL(1,𝔽5) | semidirect |
| 30. C52×C37 | C32×C4 | semidirect |
| 36. C3×C5×C37 | C3×AGL(1,𝔽5) | semidirect |
| 37. C3×C5×C37 | C3×AGL(1,𝔽5) | semidirect |
| 39. C5×C37⋊C3 | C3×AGL(1,𝔽5) | semidirect |
| 40. C5×C37⋊C3 | C3×AGL(1,𝔽5) | semidirect |
| 47. C3×C37⋊C3 | #1044 | semidirect |
| 54. C5×C37 | C32×AGL(1,𝔽5) | semidirect |
| 55. C5×C37 | C32×AGL(1,𝔽5) | semidirect |
| 61. C3×C37 | C3×#1044 | semidirect |
| 62. C37⋊C3 | C3×#1044 | semidirect |
| 68. C3×C52 | #3866⋊C3 | semidirect |
| 78. C37 | C32×#1044 | semidirect |
| 86. C52 | C3×#3866⋊C3 | semidirect |
| 94. C3×C5 | #10625191⋊C3 | semidirect |
| 95. C3×C5 | #10625192⋊C3 | semidirect |
| 105. C5 | C3×#10625191⋊C3 | semidirect |
| 106. C5 | C3×#10625192⋊C3 | semidirect |
| 109. C3 | #16814881⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C5⋊(C5⋊(D37⋊C3)) | 2 |
| C3×#16814881 | 3 |
| #16814881⋊C3 | 3 |
| C3×#10625192⋊C3 | 5 |
| C3×#10625191⋊C3 | 5 |
| C32×#1044 | 37 |