Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
2300 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 2300 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C32 | C3⋊D32 |
| commutator, cosocle, hypocenter | H(5,𝔽3) | C22×C3 |
| Frattini | C3 | C3×C3⋊D32 |
| Fitting | C3×H(5,𝔽3) | C22 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C32 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#92404 | C2 | semidirect |
| 2. C3×#92392 | C2 | semidirect |
| 3. #11758087 | C3 | direct (N × H) |
| 5. C3×H(5,𝔽3) | C22 | semidirect |
| 6. #92404 | C2×C3 | semidirect |
| 10. #92392 | C2×C3 | semidirect |
| 11. C32×#272 | D3 | semidirect |
| 18. H(5,𝔽3) | C22×C3 | semidirect |
| 20. C32×H(3,𝔽3) | C2×D3 | semidirect |
| 31. C3×#272 | C3×D3 | semidirect |
| 32. C3×#272 | C3⋊D3 | semidirect |
| 40. C34 | D32 | semidirect |
| 51. C3×H(3,𝔽3) | C2×C3×D3 | semidirect |
| 69. #272 | C3×C3⋊D3 | semidirect |
| 81. C33 | C3×D32 | semidirect |
| 134. C3 | #11758087 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#92404 | 2 |
| C3×#92392 | 2 |
| #11758087 | 3 |
| C3×D3×#272 | 3 |