Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
221 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 221 conjugacy classes of subgroups — too many to draw. Only its 37 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×#272 | C2 | semidirect |
| 2. C2×((C3⋊D3)⋊C3)⋊C2 | C2 | semidirect |
| 3. #638⋊C3 | C2 | semidirect |
| 4. #6200 | C2 | semidirect |
| 5. #6199 | C2 | semidirect |
| 7. C22×H(3,𝔽3) | C22 | semidirect |
| 10. C2×#272 | C22 | semidirect |
| 11. C2×(C3⋊D3)⋊C3 | C22 | semidirect |
| 13. (C3⋊Dic3)⋊C3 | C22 | semidirect |
| 17. #638 | D3 | semidirect |
| 25. #272 | D4 | semidirect |
| 30. C22×C32 | C2×D3 | semidirect |
| 31. C2×C3⋊D3 | C2×D3 | semidirect |
| 40. C3⋊Dic3 | C2×D3 | semidirect |
| 42. H(3,𝔽3) | C2×D4 | semidirect |
| 88. C32 | D3×D4 | semidirect |
| 114. 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×#272 | 2 |
| C2×((C3⋊D3)⋊C3)⋊C2 | 2 |
| #638⋊C3 | 2 |
| #6200 | 2 |
| #6199 | 2 |
| D3×#67 | 3 |