Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
362 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | C3⋊(D27⋊C3) |
| commutator, cosocle, hypocenter | C3×C27 | C2×C32 |
| Frattini | C9 | C32×C3⋊D3 |
| Fitting | C32×C27⋊C3 | C2 |
| socle | C33 | C3×D9 |
| LCS | G ▷ C3×C27 | |
| UCS | C1 ◁ C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C32×C27⋊C3 | C2 | semidirect |
| 3. C3⋊(D27⋊C3) | C3 | direct (N × H) |
| 4. C3×C3⋊D27 | C3 | semidirect |
| 10. C3×C27⋊C3 | D3 | semidirect |
| 11. C3×C27⋊C3 | C2×C3 | semidirect |
| 13. C32×C27 | C2×C3 | semidirect |
| 19. C3⋊D27 | C32 | semidirect |
| 36. C27⋊C3 | C3×D3 | semidirect |
| 42. C3×C27 | C3×D3 | semidirect |
| 43. C3×C27 | C2×C32 | semidirect |
| 81. C27 | C32×D3 | semidirect |
| 99. C32 | D27⋊C3 | semidirect |
| 117. C3 | C3×D27⋊C3 | semidirect |
| 118. C3 | C3⋊(D27⋊C3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C27⋊C3 | 2 |
| C32×C3⋊D9 | 3 |
| C3⋊(D27⋊C3) | 3 |
| C3×C3⋊D27 | 3 |
| C3×D27⋊C3 | 3 |