Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
221 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 221 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×H(3,𝔽3) | C2 | semidirect |
| 2. C22×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. #638⋊C3 | C2 | direct (N × H) |
| 4. C2×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 5. C2×#638 | C3 | semidirect |
| 9. C22×H(3,𝔽3) | C22 | semidirect |
| 11. C2×(C3⋊D3)⋊C3 | C22 | semidirect |
| 12. (C3⋊Dic3)⋊C3 | C22 | semidirect |
| 14. C23×C32 | D3 | semidirect |
| 15. C23×C32 | C2×C3 | semidirect |
| 16. C22×C3⋊D3 | C2×C3 | semidirect |
| 18. #638 | C2×C3 | semidirect |
| 19. C2×C3⋊Dic3 | C2×C3 | semidirect |
| 23. C2×H(3,𝔽3) | D4 | semidirect |
| 35. C22×C32 | C2×D3 | semidirect |
| 37. C22×C32 | C22×C3 | semidirect |
| 39. C2×C3⋊D3 | C22×C3 | semidirect |
| 42. C3⋊Dic3 | C22×C3 | semidirect |
| 44. H(3,𝔽3) | C2×D4 | semidirect |
| 63. C2×C32 | #67 | semidirect |
| 64. C2×C32 | C3×D4 | semidirect |
| 92. C32 | C2×#67 | semidirect |
| 93. C32 | C2×C3×D4 | semidirect |
| 95. C23 | (C3⋊D3)⋊C3 | semidirect |
| 117. C22 | C2×(C3⋊D3)⋊C3 | semidirect |
| 125. C2 | #638⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×H(3,𝔽3) | 2 |
| C22×(C3⋊D3)⋊C3 | 2 |
| #638⋊C3 | 2 |
| C2×(C3⋊Dic3)⋊C3 | 2 |
| C2×#638 | 3 |
| C2×C3×#67 | 3 |