Finite Group DatabasebetaFinite Group DatabasebetaOrder 33300.
124 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C52×C37 | C3×C4 |
| prime radical | C3×C5×C5⋊(D37⋊C3) | C2 |
| cosocle | C3×C5×D185 | C2×C3 |
| LCS | G ▷ C3×C52×C37 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊#16814884 | C3 | semidirect |
| 4. C3×C52×C37⋊C3 | C4 | semidirect |
| 14. C52×C37⋊C3 | Dic3 | semidirect |
| 15. C3×C52×C37 | C3×C4 | semidirect |
| 22. C3×C5×C37⋊C3 | Dic5 | semidirect |
| 23. C3×C5×C37⋊C3 | AGL(1,𝔽5) | semidirect |
| 31. C52×C37 | C3×Dic3 | semidirect |
| 37. C3×C5×C37 | C3×Dic5 | semidirect |
| 38. C3×C5×C37 | C3×AGL(1,𝔽5) | semidirect |
| 43. C5×C37⋊C3 | Dic15 | semidirect |
| 44. C5×C37⋊C3 | ΓL(1,𝔽16) | semidirect |
| 50. C3×C37⋊C3 | #1042 | semidirect |
| 58. C5×C37 | C3×Dic15 | semidirect |
| 59. C5×C37 | C3×ΓL(1,𝔽16) | semidirect |
| 66. C3×C37 | C3×#1042 | semidirect |
| 68. C37⋊C3 | C3⋊#1042 | semidirect |
| 74. C3×C52 | #3866⋊C3 | semidirect |
| 84. C37 | C3×C3⋊#1042 | semidirect |
| 92. C52 | C3⋊(#3866⋊C3) | semidirect |
| 103. C3×C5 | #10625191⋊C3 | semidirect |
| 104. C3×C5 | #10625194⋊C3 | semidirect |
| 114. C5 | C3⋊(#10625191⋊C3) | semidirect |
| 115. C5 | C3⋊(#10625194⋊C3) | semidirect |
| 119. C3 | #16814884⋊C3 | semidirect |
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⋊#16814884 | 3 |
| #16814884⋊C3 | 3 |
| C3⋊(#10625194⋊C3) | 5 |
| C3⋊(#10625191⋊C3) | 5 |
| C3×C3⋊#1042 | 37 |