Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
306 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D32 |
| commutator, cosocle | C2×C32 | C23×C3 |
| Frattini | C2 | C2×C3×D32 |
| Fitting, socle | C22×C33 | C22 |
| hypocenter | C32 | C2×C3×D4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C22×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C32×D3 | C2 | semidirect |
| 2. C2×C3×C3⋊Dic3 | C2 | semidirect |
| 3. C3×#625 | C2 | direct (N × H) |
| 5. C2×#625 | C3 | direct (N × H) |
| 8. C2×C32×D3 | C22 | semidirect |
| 9. C3×C3⋊Dic3 | C22 | semidirect |
| 12. C22×C3×D3 | D3 | semidirect |
| 13. C22×C3×D3 | C2×C3 | semidirect |
| 14. C2×C3⋊Dic3 | C2×C3 | semidirect |
| 18. #625 | C2×C3 | direct (N × H) |
| 19. C2×C33 | D4 | semidirect |
| 35. C2×C3×D3 | C2×D3 | semidirect |
| 36. C2×C3×D3 | C22×C3 | semidirect |
| 37. C3⋊Dic3 | C22×C3 | semidirect |
| 40. C33 | C2×D4 | semidirect |
| 44. C22×D3 | C3×D3 | semidirect |
| 57. C2×C32 | #67 | semidirect |
| 58. C2×C32 | C3×D4 | semidirect |
| 77. C2×D3 | C2×C3×D3 | semidirect |
| 84. C32 | C2×#67 | semidirect |
| 85. C32 | C2×C3×D4 | semidirect |
| 98. C2×C3 | #625 | direct (N × H) |
| 99. C2×C3 | C3×#67 | semidirect |
| 110. C3 | C2×#625 | direct (N × H) |
| 111. C3 | C2×C3×#67 | semidirect |
| 113. C2 | C3×#625 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D3 | 2 |
| C2×C3×C3⋊Dic3 | 2 |
| C3×#625 | 2 |
| C2×C3×#67 | 3 |
| C2×#625 | 3 |