Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
947 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 947 conjugacy classes of subgroups — too many to draw. Only its 120 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. C3×C3⋊#1084 | C2 | semidirect |
| 3. C32×#1084 | C2 | semidirect |
| 6. D3×#1084 | C3 | direct (N × H) |
| 8. C3×D3×H(3,𝔽3) | C4 | semidirect |
| 15. C3⋊#1084 | C2×C3 | semidirect |
| 19. C3×#1084 | D3 | direct (N × H) |
| 20. C3×#1084 | C2×C3 | semidirect |
| 21. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 28. C33×D3 | Dic3 | semidirect |
| 37. D3×H(3,𝔽3) | C3×C4 | semidirect |
| 58. #1084 | C3×D3 | direct (N × H) |
| 59. C34 | C2×Dic3 | semidirect |
| 64. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 65. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 84. C32×D3 | C3×Dic3 | semidirect |
| 125. C33 | D3×Dic3 | semidirect |
| 126. C33 | C2×C3×Dic3 | semidirect |
| 132. H(3,𝔽3) | C3×C4×D3 | semidirect |
| 160. C3×D3 | #1084 | direct (N × H) |
| 191. C32 | C2×#1084 | semidirect |
| 192. C32 | C3×D3×Dic3 | semidirect |
| 209. D3 | C3×#1084 | direct (N × H) |
| 219. C3 | D3×#1084 | direct (N × H) |
| 220. C3 | C2×C3×#1084 | 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 |
| C3×C3⋊#1084 | 2 |
| C32×#1084 | 2 |
| C32×D3×Dic3 | 3 |
| C2×C3×#1084 | 3 |
| D3×#1084 | 3 |