Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
836 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 836 conjugacy classes of subgroups — too many to draw. Only its 129 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×#92392 | C2 | semidirect |
| 2. C4×H(5,𝔽3) | C2 | semidirect |
| 3. C3×C4⋊#272 | C3 | semidirect |
| 7. C2×C3×#272 | C2×C3 | semidirect |
| 10. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 11. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 12. H(5,𝔽3) | D4 | semidirect |
| 15. C4⋊#272 | C32 | semidirect |
| 23. C33×C4 | C3×D3 | semidirect |
| 32. C3×H(3,𝔽3) | D12 | semidirect |
| 33. C3×H(3,𝔽3) | C3×D4 | semidirect |
| 56. C33 | C3×D12 | semidirect |
| 94. C4 | #92392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92392 | 2 |
| C4×H(5,𝔽3) | 2 |
| C3×C4⋊#272 | 3 |
| D12×H(3,𝔽3) | 3 |