Finite Group DatabasebetaFinite Group DatabasebetaOrder 33300.
160 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 38 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 | C3⋊#16814881 |
| commutator, hypocenter | C3×C52×C37 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C37 | C4 |
| prime radical | C32×C5⋊D185 | C2 |
| cosocle | C3×C5⋊D185 | C2×C3 |
| LCS | G ▷ C3×C52×C37 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊#16814881 | C3 | direct (N × H) |
| 4. C32×C52×C37 | C4 | semidirect |
| 15. C3×C52×C37 | Dic3 | semidirect |
| 16. C3×C52×C37 | C3×C4 | semidirect |
| 23. C32×C5×C37 | AGL(1,𝔽5) | semidirect |
| 24. C32×C5×C37 | AGL(1,𝔽5) | semidirect |
| 35. C52×C37 | C3×Dic3 | semidirect |
| 45. C3×C5×C37 | C3×AGL(1,𝔽5) | semidirect |
| 46. C3×C5×C37 | C3×AGL(1,𝔽5) | semidirect |
| 47. C3×C5×C37 | ΓL(1,𝔽16) | semidirect |
| 48. C3×C5×C37 | ΓL(1,𝔽16) | semidirect |
| 55. C32×C37 | #1044 | semidirect |
| 58. C32×C52 | #3866 | semidirect |
| 63. C5×C37 | C3×ΓL(1,𝔽16) | semidirect |
| 64. C5×C37 | C3×ΓL(1,𝔽16) | semidirect |
| 72. C3×C37 | C3×#1044 | semidirect |
| 73. C3×C37 | C3⋊#1044 | semidirect |
| 79. C3×C52 | C3×#3866 | semidirect |
| 80. C3×C52 | C3⋊#3866 | semidirect |
| 88. C32×C5 | #10625191 | semidirect |
| 89. C32×C5 | #10625192 | semidirect |
| 90. C37 | C3×C3⋊#1044 | semidirect |
| 101. C52 | C3×C3⋊#3866 | semidirect |
| 110. C3×C5 | C3×#10625191 | semidirect |
| 111. C3×C5 | C3×#10625192 | semidirect |
| 112. C3×C5 | C3⋊#10625191 | semidirect |
| 113. C3×C5 | C3⋊#10625192 | semidirect |
| 119. C32 | #16814881 | semidirect |
| 124. C5 | C3×C3⋊#10625191 | semidirect |
| 125. C5 | C3×C3⋊#10625192 | semidirect |
| 128. C3 | C3×#16814881 | semidirect |
| 129. C3 | C3⋊#16814881 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C5⋊D185 | 2 |
| C3⋊#16814881 | 3 |
| C3×#16814881 | 3 |
| C3×C3⋊#10625192 | 5 |
| C3×C3⋊#10625191 | 5 |
| C3×C3⋊#1044 | 37 |