Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
233 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 233 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 | C2×C9 | #127⋊C3 |
| commutator, hypocenter | #95 | C2×C3×C9 |
| Frattini, socle | C23×C3 | C2×C3×A4 |
| Fitting | C9×#392 | C3 |
| prime radical | C3×#392⋊C3 | C3 |
| cosocle | C3×#95 | C2×C32 |
| LCS | G ▷ #95 | |
| UCS | C1 ◁ C2×C9 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C9×#95⋊C3 | C2 | semidirect |
| 3. C9×#392 | C3 | semidirect |
| 4. #392⋊C9 | C3 | semidirect |
| 13. #392⋊C3 | C9 | direct (N × H) |
| 27. #95⋊C3 | C2×C9 | semidirect |
| 40. #392 | C3×C9 | semidirect |
| 104. C9 | #392⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#95⋊C3 | 2 |
| C3×#392⋊C3 | 3 |
| C9×#392 | 3 |
| #392⋊C9 | 3 |
| C4×C9×A4 | 4 |