Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1104 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 1104 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 2. C32×C4×H(3,𝔽3) | C2 | semidirect |
| 3. H(3,𝔽3)×C3⋊Dic3 | C2 | semidirect |
| 4. C32×C4×C3⋊D3 | C3 | semidirect |
| 7. C3⋊D3×H(3,𝔽3) | C4 | direct (N × H) |
| 9. C34×C4 | C2×C3 | semidirect |
| 10. C32×C3⋊Dic3 | C2×C3 | semidirect |
| 13. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 15. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 21. C32×C3⋊D3 | C3×C4 | semidirect |
| 31. C33×C4 | C3×D3 | semidirect |
| 40. C4×H(3,𝔽3) | C3⋊D3 | direct (N × H) |
| 41. C34 | C2×C3×C4 | semidirect |
| 43. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 45. C4×C3⋊D3 | H(3,𝔽3) | direct (N × H) |
| 71. C32×C4 | C2×H(3,𝔽3) | semidirect |
| 73. C32×C4 | C3×C3⋊D3 | semidirect |
| 74. C3⋊Dic3 | C2×H(3,𝔽3) | semidirect |
| 80. C33 | C3×C4×D3 | semidirect |
| 84. H(3,𝔽3) | C4×C3⋊D3 | direct (N × H) |
| 98. C3⋊D3 | C4×H(3,𝔽3) | direct (N × H) |
| 109. C3×C4 | D3×H(3,𝔽3) | semidirect |
| 118. C32 | C2×C4×H(3,𝔽3) | semidirect |
| 120. C32 | C3×C4×C3⋊D3 | semidirect |
| 132. C4 | C3⋊D3×H(3,𝔽3) | direct (N × H) |
| 136. C3 | C4×D3×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 |
| C32×C4×H(3,𝔽3) | 2 |
| H(3,𝔽3)×C3⋊Dic3 | 2 |
| C32×C4×C3⋊D3 | 3 |
| C4×D3×H(3,𝔽3) | 3 |