Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1488 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1488 conjugacy classes of subgroups — too many to draw. Only its 147 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. C22×C32×H(3,𝔽3) | C2 | semidirect |
| 2. C2×C3⋊D3×H(3,𝔽3) | C2 | semidirect |
| 3. H(3,𝔽3)×C3⋊Dic3 | C2 | semidirect |
| 4. C32×#638 | C3 | semidirect |
| 9. C22×C34 | C2×C3 | semidirect |
| 10. C2×C32×C3⋊D3 | C2×C3 | semidirect |
| 11. C32×C3⋊Dic3 | C2×C3 | semidirect |
| 13. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 16. C32×H(3,𝔽3) | D4 | semidirect |
| 32. C22×C33 | C3×D3 | semidirect |
| 43. C22×H(3,𝔽3) | C3⋊D3 | semidirect |
| 45. C34 | C3×D4 | semidirect |
| 47. C3×H(3,𝔽3) | #67 | semidirect |
| 49. #638 | H(3,𝔽3) | direct (N × H) |
| 79. C22×C32 | C2×H(3,𝔽3) | semidirect |
| 81. C22×C32 | C3×C3⋊D3 | semidirect |
| 82. C2×C3⋊D3 | C2×H(3,𝔽3) | semidirect |
| 86. C3⋊Dic3 | C2×H(3,𝔽3) | semidirect |
| 92. C33 | C3×#67 | semidirect |
| 96. H(3,𝔽3) | #638 | direct (N × H) |
| 127. C22×C3 | D3×H(3,𝔽3) | semidirect |
| 139. C32 | D4×H(3,𝔽3) | semidirect |
| 141. C32 | C3×#638 | semidirect |
| 157. C22 | C3⋊D3×H(3,𝔽3) | semidirect |
| 162. 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 |
|---|---|
| C22×C32×H(3,𝔽3) | 2 |
| C2×C3⋊D3×H(3,𝔽3) | 2 |
| H(3,𝔽3)×C3⋊Dic3 | 2 |
| C32×#638 | 3 |
| #67×H(3,𝔽3) | 3 |