Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
162 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D32 |
| commutator | C2×C32 | C2×C3×C4 |
| Frattini | C22 | C3×D32 |
| Fitting, socle, prime radical | C22×C33 | C22 |
| cosocle | C22×C32 | C22×C3 |
| hypocenter | C32 | C3×C4⋊C4 |
| LCS | G ▷ C2×C32 ▷ C32 | |
| UCS | C1 ◁ C22×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #3724 | C3 | direct (N × H) |
| 6. C3×C3⋊Dic3 | C4 | semidirect |
| 26. C3⋊Dic3 | C3×C4 | semidirect |
| 32. C33 | C4⋊C4 | semidirect |
| 71. C32 | Dic3⋊C4 | semidirect |
| 72. C32 | C3×C4⋊C4 | semidirect |
| 96. C3 | #3724 | direct (N × H) |
| 97. C3 | C3×Dic3⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊Dic3 | 2 |
| C2×C32×Dic3 | 2 |
| C3×Dic3⋊C4 | 3 |
| #3724 | 3 |