Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1011 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 1011 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
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. C32×#1084 | C2 | semidirect |
| 6. #10619892 | C3 | direct (N × H) |
| 11. C2×C33×D3 | D3 | semidirect |
| 14. C2×C3⋊#272 | C2×C3 | semidirect |
| 18. C2×D3×H(3,𝔽3) | C2×C3 | semidirect |
| 20. C3×#1084 | D3 | semidirect |
| 21. C3×#1084 | C2×C3 | semidirect |
| 22. C32×H(3,𝔽3) | D4 | semidirect |
| 51. C2×C32×D3 | C3×D3 | semidirect |
| 63. #1084 | C3×D3 | semidirect |
| 64. C34 | #67 | semidirect |
| 69. C3×H(3,𝔽3) | D12 | semidirect |
| 70. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 119. C2×C3×D3 | #272 | semidirect |
| 137. C33 | #626 | semidirect |
| 138. C33 | C3×#67 | semidirect |
| 144. H(3,𝔽3) | C3×D12 | semidirect |
| 191. C2×D3 | C3×#272 | semidirect |
| 211. C32 | #6235 | semidirect |
| 212. C32 | C3×#626 | semidirect |
| 244. C3 | #10619892 | direct (N × H) |
| 245. C3 | C3×#6235 | 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 |
| C32×#1084 | 2 |
| C32×#626 | 3 |
| C3×#6235 | 3 |
| #10619892 | 3 |