Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
892 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 892 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×#272 | C2 | semidirect |
| 2. C2×C32×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. C32×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 6. C3×#6200 | C3 | direct (N × H) |
| 10. C2×C32×C3⋊D3 | D3 | semidirect |
| 15. C32×C3⋊Dic3 | D3 | semidirect |
| 17. C2×C3×#272 | C2×C3 | semidirect |
| 19. C2×C3×(C3⋊D3)⋊C3 | C2×C3 | semidirect |
| 21. C3×(C3⋊Dic3)⋊C3 | C2×C3 | semidirect |
| 22. C32×H(3,𝔽3) | D4 | semidirect |
| 28. #6200 | C32 | direct (N × H) |
| 46. C2×C3×C3⋊D3 | C3×D3 | semidirect |
| 61. C3×C3⋊Dic3 | C3×D3 | semidirect |
| 66. C2×#272 | C2×C32 | semidirect |
| 68. C2×(C3⋊D3)⋊C3 | C2×C32 | semidirect |
| 70. (C3⋊Dic3)⋊C3 | C2×C32 | semidirect |
| 72. C34 | D12 | semidirect |
| 73. C34 | #67 | semidirect |
| 77. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 127. C2×C3⋊D3 | C32×D3 | semidirect |
| 144. C3⋊Dic3 | C32×D3 | semidirect |
| 160. C33 | C3×D12 | semidirect |
| 161. C33 | C3×#67 | semidirect |
| 166. H(3,𝔽3) | C32×D4 | semidirect |
| 245. C32 | #6200 | direct (N × H) |
| 247. C32 | C32×D12 | semidirect |
| 248. C32 | C32×#67 | semidirect |
| 280. C3 | C3×#6200 | 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 |
| C2×C32×(C3⋊D3)⋊C3 | 2 |
| C32×(C3⋊Dic3)⋊C3 | 2 |
| C32×#626 | 3 |
| C32×#625 | 3 |
| C3×#6200 | 3 |