Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1403 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 1403 conjugacy classes of subgroups — too many to draw. Only its 352 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. C3×Dic3×H(3,𝔽3) | C2 | semidirect |
| 4. C33×C4×D3 | C3 | semidirect |
| 6. C4×D3×H(3,𝔽3) | C3 | direct (N × H) |
| 8. C3×D3×H(3,𝔽3) | C4 | direct (N × H) |
| 10. C34×C4 | C2×C3 | semidirect |
| 11. C33×Dic3 | C2×C3 | semidirect |
| 17. C3×C4×H(3,𝔽3) | D3 | direct (N × H) |
| 18. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 19. Dic3×H(3,𝔽3) | C2×C3 | semidirect |
| 20. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 24. C32×C4×D3 | C32 | semidirect |
| 27. C33×D3 | C3×C4 | semidirect |
| 33. D3×H(3,𝔽3) | C3×C4 | direct (N × H) |
| 43. C33×C4 | C3×D3 | semidirect |
| 45. C33×C4 | C2×C32 | semidirect |
| 48. C32×Dic3 | C2×C32 | semidirect |
| 52. C4×H(3,𝔽3) | C3×D3 | direct (N × H) |
| 53. C34 | C2×C3×C4 | semidirect |
| 56. C3×H(3,𝔽3) | C4×D3 | direct (N × H) |
| 57. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 62. C3×C4×D3 | H(3,𝔽3) | direct (N × H) |
| 74. C32×D3 | C32×C4 | semidirect |
| 95. C32×C4 | C2×H(3,𝔽3) | semidirect |
| 97. C32×C4 | C32×D3 | semidirect |
| 100. C3×Dic3 | C2×H(3,𝔽3) | semidirect |
| 106. C33 | C3×C4×D3 | semidirect |
| 108. C33 | C2×C32×C4 | semidirect |
| 110. H(3,𝔽3) | C3×C4×D3 | direct (N × H) |
| 114. C4×D3 | C3×H(3,𝔽3) | direct (N × H) |
| 131. C3×D3 | C4×H(3,𝔽3) | direct (N × H) |
| 144. C3×C4 | D3×H(3,𝔽3) | direct (N × H) |
| 145. C3×C4 | C2×C3×H(3,𝔽3) | semidirect |
| 147. Dic3 | C2×C3×H(3,𝔽3) | semidirect |
| 156. C32 | C2×C4×H(3,𝔽3) | semidirect |
| 158. C32 | C32×C4×D3 | semidirect |
| 171. D3 | C3×C4×H(3,𝔽3) | direct (N × H) |
| 174. C4 | C3×D3×H(3,𝔽3) | direct (N × H) |
| 179. C3 | C4×D3×H(3,𝔽3) | direct (N × H) |
| 180. C3 | C2×C3×C4×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 |
| C3×Dic3×H(3,𝔽3) | 2 |
| C33×C4×D3 | 3 |
| C2×C3×C4×H(3,𝔽3) | 3 |
| C4×D3×H(3,𝔽3) | 3 |