Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
849 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 849 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C3 | C32×D32 |
| commutator, socle, cosocle | C2×C33 | C22×C32 |
| Fitting | C2×C32×H(3,𝔽3) | C22 |
| hypercenter | C2×H(3,𝔽3) | D32 |
| hypocenter | C32 | D4×H(3,𝔽3) |
| LCS | G ▷ C2×C33 ▷ C32 | |
| UCS | C1 ◁ C2×C3 ◁ C2×H(3,𝔽3) | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×D3×H(3,𝔽3) | C2 | semidirect |
| 2. H(3,𝔽3)×C3⋊Dic3 | C2 | semidirect |
| 3. C32×#625 | C3 | semidirect |
| 7. C2×C33×D3 | C2×C3 | semidirect |
| 8. C32×C3⋊Dic3 | C2×C3 | semidirect |
| 11. C2×D3×H(3,𝔽3) | D3 | semidirect |
| 14. C32×H(3,𝔽3) | D4 | semidirect |
| 32. C2×C32×D3 | C3×D3 | semidirect |
| 41. C34 | C3×D4 | semidirect |
| 45. C3×H(3,𝔽3) | #67 | semidirect |
| 49. #625 | H(3,𝔽3) | direct (N × H) |
| 78. C2×C3×D3 | C2×H(3,𝔽3) | semidirect |
| 81. C3⋊Dic3 | C2×H(3,𝔽3) | semidirect |
| 92. C33 | C3×#67 | semidirect |
| 97. H(3,𝔽3) | #625 | direct (N × H) |
| 132. C2×D3 | D3×H(3,𝔽3) | semidirect |
| 150. C32 | D4×H(3,𝔽3) | semidirect |
| 151. C32 | C3×#625 | semidirect |
| 176. C3 | #67×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×H(3,𝔽3) | 2 |
| H(3,𝔽3)×C3⋊Dic3 | 2 |
| C32×#625 | 3 |
| #67×H(3,𝔽3) | 3 |