Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1040 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 1040 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
| 7. C3⋊D3×H(3,𝔽3) | C4 | semidirect |
| 14. C3×#1084 | D3 | semidirect |
| 15. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 21. C32×C3⋊D3 | Dic3 | semidirect |
| 40. #1084 | C3⋊D3 | direct (N × H) |
| 41. C34 | C2×Dic3 | semidirect |
| 43. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 79. C33 | D3×Dic3 | semidirect |
| 83. H(3,𝔽3) | C4×C3⋊D3 | semidirect |
| 97. C3⋊D3 | #1084 | direct (N × H) |
| 117. C32 | C2×#1084 | semidirect |
| 119. C32 | Dic3×C3⋊D3 | semidirect |
| 135. C3 | D3×#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 |
| C3×Dic3×C3⋊D3 | 3 |
| D3×#1084 | 3 |