Finite Group DatabasebetaFinite Group DatabasebetaOrder 36900.
160 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 42 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⋊#16861523 |
| commutator, hypocenter | C3×C52×C41 | C3×C4 |
| Frattini | C1 | G |
| Fitting, socle | C32×C52×C41 | C4 |
| prime radical | C32×C41×C5⋊D5 | C2 |
| cosocle | C3×C41×C5⋊D5 | C2×C3 |
| LCS | G ▷ C3×C52×C41 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3⋊#16861523 | C3 | direct (N × H) |
| 4. C32×C52×C41 | C4 | semidirect |
| 13. C3×C52×C41 | Dic3 | semidirect |
| 14. C3×C52×C41 | C3×C4 | semidirect |
| 19. C32×C5×C41 | AGL(1,𝔽5) | semidirect |
| 27. C52×C41 | C3×Dic3 | semidirect |
| 35. C3×C5×C41 | C3×AGL(1,𝔽5) | semidirect |
| 36. C3×C5×C41 | ΓL(1,𝔽16) | semidirect |
| 42. C32×C41 | #1044 | semidirect |
| 48. C32×C52 | Dic41 | semidirect |
| 50. C5×C41 | C3×ΓL(1,𝔽16) | semidirect |
| 57. C3×C41 | C3×#1044 | semidirect |
| 58. C3×C41 | C3⋊#1044 | semidirect |
| 64. C3×C52 | C3×Dic41 | semidirect |
| 65. C3×C52 | Dic123 | semidirect |
| 70. C32×C5 | #11717963 | semidirect |
| 71. C41 | C3×C3⋊#1044 | semidirect |
| 79. C52 | C3×Dic123 | semidirect |
| 86. C3×C5 | C3×#11717963 | semidirect |
| 87. C3×C5 | C3⋊#11717963 | semidirect |
| 92. C32 | #16861523 | semidirect |
| 97. C5 | C3×C3⋊#11717963 | semidirect |
| 100. C3 | C3×#16861523 | semidirect |
| 101. C3 | C3⋊#16861523 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C41×C5⋊D5 | 2 |
| C3⋊#16861523 | 3 |
| C3×#16861523 | 3 |
| C3×C3⋊#11717963 | 5 |
| C3×C3⋊#1044 | 41 |