Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1031 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 1031 conjugacy classes of subgroups — too many to draw. Only its 116 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. C4×C32⋊H(3,𝔽3) | C2 | semidirect |
| 3. #11757642 | C2 | semidirect |
| 7. #92338 | C4 | direct (N × H) |
| 9. C34×C4 | D3 | semidirect |
| 12. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 14. C32⋊H(3,𝔽3) | C2×C4 | semidirect |
| 29. C33×C4 | C3⋊D3 | semidirect |
| 37. C34 | C4×D3 | semidirect |
| 38. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 67. C32×C4 | #272 | semidirect |
| 76. C33 | C4×C3⋊D3 | semidirect |
| 113. C32 | C4×#272 | semidirect |
| 125. C4 | #92338 | direct (N × H) |
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 |
| #11757642 | 2 |
| C32×C4×C3⋊D3 | 3 |
| C3×C4×#272 | 3 |