Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
205 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 205 conjugacy classes of subgroups — too many to draw. Only its 39 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. C22×(C3⋊D3)⋊C3 | C2 | semidirect |
| 2. C2×((C3⋊D3)⋊C3)⋊C2 | C2 | semidirect |
| 3. #6235 | C2 | semidirect |
| 4. #638⋊C3 | C2 | semidirect |
| 5. #6200 | C2 | semidirect |
| 6. #6198 | C2 | semidirect |
| 7. ((C3⋊D3)⋊C3)⋊C4 | C2 | semidirect |
| 10. C22×H(3,𝔽3) | C22 | semidirect |
| 11. C2×#272 | C22 | semidirect |
| 14. C2×(C3⋊D3)⋊C3 | C22 | semidirect |
| 15. C2×(C3⋊D3)⋊C3 | C22 | semidirect |
| 17. #1084 | C22 | semidirect |
| 18. (C3⋊Dic3)⋊C3 | C22 | semidirect |
| 19. C22×C3⋊D3 | D3 | semidirect |
| 23. #638 | D3 | semidirect |
| 39. (C3⋊D3)⋊C3 | D4 | semidirect |
| 44. C22×C32 | C2×D3 | semidirect |
| 45. C22×C32 | C2×D3 | semidirect |
| 48. C2×C3⋊D3 | C2×D3 | semidirect |
| 49. C2×C3⋊D3 | C2×D3 | semidirect |
| 59. C3⋊Dic3 | C2×D3 | semidirect |
| 64. H(3,𝔽3) | C2×D4 | semidirect |
| 95. C3⋊D3 | #67 | semidirect |
| 134. C32 | D3×D4 | semidirect |
| 135. C32 | C2×#67 | semidirect |
| 170. C22 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C3⋊D3)⋊C3 | 2 |
| C2×((C3⋊D3)⋊C3)⋊C2 | 2 |
| #6235 | 2 |
| #638⋊C3 | 2 |
| #6200 | 2 |
| #6198 | 2 |
| ((C3⋊D3)⋊C3)⋊C4 | 2 |
| #3811 | 3 |
| D3×#67 | 3 |