Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
123 conjugacy classes of subgroups; only the 19 normal subgroups are shown.
This group has 123 conjugacy classes of subgroups — too many to draw. Only its 19 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C22⋊C9 | C22 |
| Frattini | C3 | D3×S4 |
| Fitting, socle | C22×C32 | C2×D3 |
| LCS | G ▷ C3×C22⋊C9 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. D3×C22⋊C9 | C2 | semidirect |
| 2. C3⋊((C22⋊C9)⋊C2) | C2 | semidirect |
| 3. C3×(C22⋊C9)⋊C2 | C2 | semidirect |
| 6. C3×C22⋊C9 | C22 | semidirect |
| 18. (C22⋊C9)⋊C2 | D3 | direct (N × H) |
| 35. C22⋊C9 | C2×D3 | semidirect |
| 40. C22×D3 | D9 | semidirect |
| 66. C22×C3 | C2×D9 | semidirect |
| 104. D3 | (C22⋊C9)⋊C2 | direct (N × H) |
| 111. C22 | D3×D9 | semidirect |
| 115. C3 | C2×(C22⋊C9)⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×C22⋊C9 | 2 |
| C3⋊((C22⋊C9)⋊C2) | 2 |
| C3×(C22⋊C9)⋊C2 | 2 |
| D3×#67 | 3 |
| C2×(C22⋊C9)⋊C2 | 3 |
| D3×D9 | 4 |