Finite Group DatabasebetaFinite Group Databasebeta← C4×(C3⋊D3)⋊H(3,𝔽3) #14517309
Order 1944.
537 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 537 conjugacy classes of subgroups — too many to draw. Only its 86 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. (C3⋊Dic3)⋊H(3,𝔽3) | C2 | semidirect |
| 4. C32×C4×C3⋊D3 | C3 | semidirect |
| 6. C3×C4×(C3⋊D3)⋊C3 | C3 | semidirect |
| 8. (C3⋊D3)⋊H(3,𝔽3) | C4 | direct (N × H) |
| 10. C34×C4 | C2×C3 | semidirect |
| 11. C32×C3⋊Dic3 | C2×C3 | semidirect |
| 16. C3×C4×H(3,𝔽3) | D3 | semidirect |
| 17. C3×C4×H(3,𝔽3) | C2×C3 | semidirect |
| 19. C3×(C3⋊Dic3)⋊C3 | C2×C3 | semidirect |
| 20. C32⋊H(3,𝔽3) | C2×C4 | semidirect |
| 29. C32×C3⋊D3 | C3×C4 | semidirect |
| 35. C3×(C3⋊D3)⋊C3 | C3×C4 | semidirect |
| 49. C33×C4 | C3×D3 | semidirect |
| 67. C34 | C2×C3×C4 | semidirect |
| 70. C3×H(3,𝔽3) | C4×D3 | semidirect |
| 71. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 74. C4×C3⋊D3 | H(3,𝔽3) | semidirect |
| 135. C32×C4 | (C3⋊D3)⋊C3 | semidirect |
| 136. C32×C4 | C2×H(3,𝔽3) | semidirect |
| 138. C3⋊Dic3 | C2×H(3,𝔽3) | semidirect |
| 152. C33 | C3×C4×D3 | semidirect |
| 192. C3⋊D3 | C4×H(3,𝔽3) | semidirect |
| 239. C32 | C4×(C3⋊D3)⋊C3 | semidirect |
| 240. C32 | C2×C4×H(3,𝔽3) | semidirect |
| 260. C4 | (C3⋊D3)⋊H(3,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×(C3⋊D3)⋊H(3,𝔽3) | 2 |
| C4×C32⋊H(3,𝔽3) | 2 |
| (C3⋊Dic3)⋊H(3,𝔽3) | 2 |
| C32×C4×C3⋊D3 | 3 |
| C4×D3×H(3,𝔽3) | 3 |
| C3×C4×(C3⋊D3)⋊C3 | 3 |