Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
285 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 285 conjugacy classes of subgroups — too many to draw. Only its 34 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×#6856 | C2 | semidirect |
| 3. #11757282 | C2 | semidirect |
| 4. C4×C3⋊#272 | C3 | semidirect |
| 7. #92159 | C4 | direct (N × H) |
| 10. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 11. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 12. C3⋊#1084 | C2×C3 | semidirect |
| 15. #6856 | C2×C4 | semidirect |
| 23. C3⋊#272 | C3×C4 | semidirect |
| 42. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 43. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 158. C4 | #92159 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#92159 | 2 |
| C4×#6856 | 2 |
| #11757282 | 2 |
| C4×C3⋊#272 | 3 |
| C3×C4×(C3⋊D3)⋊C3 | 3 |