Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
156 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 35 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | ((C3⋊D3)⋊C3)⋊C2 |
| commutator, cosocle | C2×H(3,𝔽3) | C23 |
| Frattini, socle | C2×C3 | C2×D32 |
| Fitting | C4×H(3,𝔽3) | C22 |
| hypocenter | H(3,𝔽3) | #41 |
| LCS | G ▷ C2×H(3,𝔽3) ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×#272 | C2 | semidirect |
| 2. C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. #6200 | C2 | semidirect |
| 5. #6200 | C2 | semidirect |
| 6. #6198 | C2 | semidirect |
| 7. #6196 | C2 | semidirect |
| 17. C4×C3⋊D3 | D3 | semidirect |
| 18. C4×C3⋊D3 | D3 | semidirect |
| 56. H(3,𝔽3) | #41 | semidirect |
| 115. C32 | #235 | semidirect |
| 116. C32 | #235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#272 | 2 |
| C4×(C3⋊D3)⋊C3 | 2 |
| #6200 | 2 |
| #6198 | 2 |
| #6196 | 2 |
| #3798 | 3 |