Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
844 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 108 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×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 4. C3×#6199 | C3 | direct (N × H) |
| 6. C32×#272 | C4 | semidirect |
| 9. C32×C3⋊Dic3 | D3 | semidirect |
| 13. C3×(C3⋊Dic3)⋊C3 | C2×C3 | semidirect |
| 14. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 18. #6199 | C32 | direct (N × H) |
| 26. C3×#272 | C3×C4 | semidirect |
| 35. C3×C3⋊Dic3 | C3×D3 | semidirect |
| 42. (C3⋊Dic3)⋊C3 | C2×C32 | semidirect |
| 44. C34 | C4×D3 | semidirect |
| 47. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 72. #272 | C32×C4 | semidirect |
| 85. C3⋊Dic3 | C32×D3 | semidirect |
| 98. C33 | C3×C4×D3 | semidirect |
| 102. H(3,𝔽3) | C2×C32×C4 | semidirect |
| 152. C32 | #6199 | direct (N × H) |
| 154. C32 | C32×C4×D3 | semidirect |
| 175. C3 | C3×#6199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#272 | 2 |
| C32×(C3⋊Dic3)⋊C3 | 2 |
| C32×D3×Dic3 | 3 |
| C3×#6199 | 3 |