Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1241 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 1241 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D3×C3⋊(C3⋊D3) |
| commutator, Fitting, cosocle | C2×C32×H(3,𝔽3) | C22 |
| socle | C2×C33 | C2×C3⋊D3 |
| hypocenter | C32×H(3,𝔽3) | D4 |
| LCS | G ▷ C2×C32×H(3,𝔽3) ▷ C32×H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C3⋊#272 | C2 | semidirect |
| 2. C2×C3×D3×H(3,𝔽3) | C2 | semidirect |
| 3. C3⋊(C3⋊#1084) | C2 | semidirect |
| 11. C2×C33×D3 | D3 | semidirect |
| 14. C2×C3⋊#272 | D3 | semidirect |
| 16. C2×D3×H(3,𝔽3) | D3 | semidirect |
| 21. C32×H(3,𝔽3) | D4 | semidirect |
| 47. C2×C32×D3 | C3⋊D3 | semidirect |
| 58. C34 | #67 | semidirect |
| 61. C3×H(3,𝔽3) | #67 | semidirect |
| 62. C3×H(3,𝔽3) | #67 | semidirect |
| 106. C2×C3×D3 | #272 | semidirect |
| 124. C33 | #625 | semidirect |
| 126. C33 | #638 | semidirect |
| 128. H(3,𝔽3) | #625 | semidirect |
| 175. C2×D3 | C3⋊#272 | semidirect |
| 195. C32 | #6235 | semidirect |
| 197. C32 | #6290 | semidirect |
| 228. C3 | #10619891 | semidirect |
| 229. C3 | #10619994 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C3⋊#272 | 2 |
| C2×C3×D3×H(3,𝔽3) | 2 |
| C3⋊(C3⋊#1084) | 2 |
| C3×#6290 | 3 |
| #10619994 | 3 |
| #10619891 | 3 |