Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
290 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 96 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, hypocenter | C32 | C22×C3×C4 |
| Frattini | C2 | C2×C3×D32 |
| Fitting, socle | C22×C33 | C22 |
| prime radical | C22×C3×C3⋊D3 | C2 |
| cosocle | C2×C32 | C23×C3 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C32×Dic3 | C2 | semidirect |
| 3. C3×#624 | C2 | direct (N × H) |
| 5. C2×#624 | C3 | direct (N × H) |
| 7. C2×C3×C3⋊D3 | C4 | semidirect |
| 9. C32×Dic3 | C22 | semidirect |
| 15. C2×C3×Dic3 | D3 | semidirect |
| 16. C2×C3×Dic3 | C2×C3 | semidirect |
| 18. #624 | C2×C3 | direct (N × H) |
| 19. C2×C33 | C2×C4 | semidirect |
| 21. C3×C3⋊D3 | C2×C4 | semidirect |
| 29. C2×C3⋊D3 | C3×C4 | semidirect |
| 37. C3×Dic3 | C2×D3 | semidirect |
| 38. C3×Dic3 | C22×C3 | semidirect |
| 39. C33 | C22×C4 | semidirect |
| 47. C2×Dic3 | C3×D3 | semidirect |
| 55. C2×C32 | C4×D3 | semidirect |
| 56. C2×C32 | C2×C3×C4 | semidirect |
| 59. C3⋊D3 | C2×C3×C4 | semidirect |
| 77. Dic3 | C2×C3×D3 | semidirect |
| 81. C32 | C2×C4×D3 | semidirect |
| 82. C32 | C22×C3×C4 | semidirect |
| 93. C2×C3 | #624 | direct (N × H) |
| 94. C2×C3 | C3×C4×D3 | semidirect |
| 106. C3 | C2×#624 | direct (N × H) |
| 107. C3 | C2×C3×C4×D3 | semidirect |
| 109. C2 | C3×#624 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C3⋊D3 | 2 |
| C2×C32×Dic3 | 2 |
| C3×#624 | 2 |
| C2×C3×C4×D3 | 3 |
| C2×#624 | 3 |