Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
270 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 54 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 | C2 | D33 |
| commutator, Fitting, socle, cosocle | C2×C33 | C23 |
| hypocenter | C33 | C2×D4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×D32 | C2 | semidirect |
| 2. #6295 | C2 | semidirect |
| 3. #6290 | C2 | semidirect |
| 4. D3×C3⋊Dic3 | C2 | semidirect |
| 5. C3×#625 | C2 | semidirect |
| 8. C2×C3×C3⋊D3 | C22 | semidirect |
| 10. C2×C32×D3 | C22 | semidirect |
| 12. C3⋊(C3⋊Dic3) | C22 | semidirect |
| 13. C3×C3⋊Dic3 | C22 | semidirect |
| 16. C2×D32 | D3 | semidirect |
| 25. #625 | D3 | direct (N × H) |
| 31. C32×D3 | D4 | semidirect |
| 36. C2×C3⋊D3 | C2×D3 | semidirect |
| 45. C2×C3×D3 | C2×D3 | semidirect |
| 46. C2×C3×D3 | C2×D3 | semidirect |
| 53. C3⋊Dic3 | C2×D3 | semidirect |
| 56. C33 | C2×D4 | semidirect |
| 86. C3×D3 | #67 | semidirect |
| 101. C2×D3 | D32 | semidirect |
| 113. C32 | D3×D4 | semidirect |
| 114. C32 | C2×#67 | semidirect |
| 135. D3 | #625 | direct (N × H) |
| 145. C3 | C2×#625 | semidirect |
| 146. C3 | D3×#67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D32 | 2 |
| #6295 | 2 |
| #6290 | 2 |
| D3×C3⋊Dic3 | 2 |
| C3×#625 | 2 |
| D3×#67 | 3 |
| C2×#625 | 3 |