Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
122 conjugacy classes of subgroups; only the 31 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 31 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #6295 |
| commutator, Fitting, cosocle | C33×C4 | C22 |
| Frattini, hypercenter | C4 | #1113 |
| socle | C2×C33 | D4 |
| prime radical | C3×C4⋊(C3⋊D3) | C2 |
| hypocenter | C33 | SD16 |
| LCS | G ▷ C33×C4 ▷ C2×C33 ▷ C33 | |
| UCS | C1 ◁ C2 ◁ C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#634 | C2 | semidirect |
| 3. C3×C3⋊(C3⋊C8) | C2 | semidirect |
| 11. #634 | D3 | semidirect |
| 18. C3⋊(C3⋊C8) | D3 | semidirect |
| 42. C33 | SD16 | semidirect |
| 86. C32 | #204 | semidirect |
| 87. C32 | #214 | semidirect |
| 88. C32 | #215 | semidirect |
| 110. C3 | #3715 | semidirect |
| 111. C3 | #3716 | semidirect |
| 112. C3 | #3717 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4⋊(C3⋊D3) | 2 |
| C3×#634 | 2 |
| C3×C3⋊(C3⋊C8) | 2 |
| #3717 | 3 |
| #3716 | 3 |
| #3715 | 3 |