Finite Group DatabasebetaFinite Group DatabasebetaOrder 432.
194 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 53 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 | D3×D9 |
| commutator, cosocle | C2×C3×C9 | C23 |
| Frattini | C2×C3 | C2×D32 |
| Fitting | C22×C3×C9 | C22 |
| socle | C22×C32 | C2×D3 |
| hypocenter | C3×C9 | C2×D4 |
| LCS | G ▷ C2×C3×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3⋊D9 | C2 | semidirect |
| 2. C22×C3×D9 | C2 | semidirect |
| 3. C2×C9×Dic3 | C2 | semidirect |
| 4. #6192 | C2 | direct (N × H) |
| 9. C2×C3⋊D9 | C22 | semidirect |
| 11. C2×C3×D9 | C22 | semidirect |
| 12. C9×Dic3 | C22 | semidirect |
| 19. C22×D9 | D3 | semidirect |
| 22. C2×C3×C9 | D4 | semidirect |
| 41. C2×D9 | C2×D3 | semidirect |
| 43. C3×C9 | C2×D4 | semidirect |
| 51. C2×Dic3 | D9 | semidirect |
| 59. C2×C9 | #67 | semidirect |
| 79. Dic3 | C2×D9 | semidirect |
| 82. C9 | C2×#67 | semidirect |
| 90. C2×C3 | D36 | semidirect |
| 105. C3 | C2×D36 | semidirect |
| 109. C2 | #6192 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊D9 | 2 |
| C22×C3×D9 | 2 |
| C2×C9×Dic3 | 2 |
| #6192 | 2 |
| C2×#626 | 3 |
| C2×D36 | 3 |