Finite Group DatabasebetaFinite Group Databasebeta← C2×(C3×A4)⋊H(3,𝔽3) #14518425
Order 1944.
980 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 980 conjugacy classes of subgroups — too many to draw. Only its 118 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. (C3×A4)⋊H(3,𝔽3) | C2 | direct (N × H) |
| 2. C2×C33×A4 | C3 | semidirect |
| 3. C23×C3×H(3,𝔽3) | C3 | semidirect |
| 4. C2×C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 5. C2×C3×C22⋊H(3,𝔽3) | C3 | semidirect |
| 7. C33×A4 | C2×C3 | semidirect |
| 10. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 11. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 12. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 15. C23×C33 | C32 | semidirect |
| 19. C2×C32×A4 | C32 | semidirect |
| 28. C2×C3×H(3,𝔽3) | A4 | semidirect |
| 34. C22×C33 | C2×C32 | semidirect |
| 38. C32×A4 | C2×C32 | semidirect |
| 47. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 51. C23×C32 | H(3,𝔽3) | semidirect |
| 58. C2×C3×A4 | H(3,𝔽3) | semidirect |
| 68. C2×C33 | C3×A4 | semidirect |
| 87. C22×C32 | C2×H(3,𝔽3) | semidirect |
| 94. C3×A4 | C2×H(3,𝔽3) | semidirect |
| 100. C33 | C2×C3×A4 | semidirect |
| 129. C2×C32 | C22⋊H(3,𝔽3) | semidirect |
| 154. C32 | C2×C22⋊H(3,𝔽3) | semidirect |
| 156. C23 | C32⋊H(3,𝔽3) | semidirect |
| 173. C22 | C2×C32⋊H(3,𝔽3) | semidirect |
| 182. C2 | (C3×A4)⋊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 |
|---|---|
| (C3×A4)⋊H(3,𝔽3) | 2 |
| C2×C33×A4 | 3 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C3×C22⋊H(3,𝔽3) | 3 |
| C2×C32⋊H(3,𝔽3) | 4 |