Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
152 conjugacy classes of subgroups; only the 22 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 22 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 | D3×#157 |
| commutator, Fitting, socle | C2×C33 | C2×C4 |
| prime radical | C2×D3×C3⋊D3 | C2 |
| cosocle | C2×C3×C3⋊D3 | C22 |
| hypocenter | C33 | C22⋊C4 |
| LCS | G ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3⋊#157 | C2 | semidirect |
| 3. C2×C3×#157 | C2 | semidirect |
| 5. C2×C3⋊(C3⋊D3) | C4 | semidirect |
| 7. C2×C32×D3 | C4 | semidirect |
| 15. C2×#157 | D3 | semidirect |
| 35. C33 | C22⋊C4 | semidirect |
| 63. C2×D3 | #157 | semidirect |
| 68. C32 | (C2×D3)⋊C4 | semidirect |
| 93. C3 | C22⋊#157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C3⋊D3 | 2 |
| C2×C3⋊#157 | 2 |
| C2×C3×#157 | 2 |
| C22⋊#157 | 3 |
| (C2×D3)⋊C4 | 9 |