Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
836 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 1. C2×C32×(C3⋊D3)⋊C3 | C2 | semidirect |
| 2. C32×#1084 | C2 | semidirect |
| 4. C3×#6198 | C3 | direct (N × H) |
| 7. C2×C32×C3⋊D3 | D3 | semidirect |
| 12. C2×C3×(C3⋊D3)⋊C3 | C2×C3 | semidirect |
| 13. C3×#1084 | C2×C3 | semidirect |
| 14. C32×H(3,𝔽3) | D4 | semidirect |
| 18. #6198 | C32 | direct (N × H) |
| 29. C2×C3×C3⋊D3 | C3×D3 | semidirect |
| 42. C2×(C3⋊D3)⋊C3 | C2×C32 | semidirect |
| 43. #1084 | C2×C32 | semidirect |
| 45. C34 | #67 | semidirect |
| 48. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 77. C2×C3⋊D3 | C32×D3 | semidirect |
| 99. C33 | C3×#67 | semidirect |
| 103. H(3,𝔽3) | C32×D4 | semidirect |
| 152. C32 | #6198 | direct (N × H) |
| 154. C32 | C32×#67 | semidirect |
| 175. C3 | C3×#6198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×(C3⋊D3)⋊C3 | 2 |
| C32×#1084 | 2 |
| C32×#626 | 3 |
| C3×#6198 | 3 |