Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1031 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 1031 conjugacy classes of subgroups — too many to draw. Only its 114 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×#92338 | C2 | semidirect |
| 2. C4×C32⋊H(3,𝔽3) | C2 | semidirect |
| 8. C34×C4 | D3 | semidirect |
| 10. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 11. C32⋊H(3,𝔽3) | D4 | semidirect |
| 26. C33×C4 | C3⋊D3 | semidirect |
| 30. C34 | D12 | semidirect |
| 31. C3×H(3,𝔽3) | D12 | semidirect |
| 59. C32×C4 | #272 | semidirect |
| 64. C33 | C4⋊(C3⋊D3) | semidirect |
| 98. C32 | C4⋊#272 | semidirect |
| 109. C4 | #92338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92338 | 2 |
| C4×C32⋊H(3,𝔽3) | 2 |
| C32×C4⋊(C3⋊D3) | 3 |
| C3×C4⋊#272 | 3 |