Finite Group DatabasebetaFinite Group DatabasebetaOrder 1458.
224 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 27 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C3 | C3×#4177 |
| commutator, cosocle | C32×C9 | C2×C32 |
| Frattini | C33 | C32×D3 |
| Fitting | #10624731 | C2 |
| socle | C32 | C3×(C3⋊D3)⋊C3 |
| hypercenter | C32 | #4177 |
| hypocenter | C3×C9 | C2×H(3,𝔽3) |
| LCS | G ▷ C32×C9 ▷ C3×C9 | |
| UCS | C1 ◁ C3 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10624731 | C2 | semidirect |
| 2. C32×C3⋊D9 | C3 | semidirect |
| 3. C3×#4177 | C3 | semidirect |
| 5. C33×C9 | C2×C3 | semidirect |
| 7. C3×#731 | C2×C3 | semidirect |
| 40. C3⋊D9 | H(3,𝔽3) | semidirect |
| 73. C3×C9 | C2×H(3,𝔽3) | semidirect |
| 101. C32 | #4177 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624731 | 2 |
| C32×C3⋊D9 | 3 |
| C3×#4177 | 3 |
| (C3⋊D3)⋊H(3,𝔽3) | 3 |