Finite Group DatabasebetaFinite Group Databasebeta← (C3×(C3⋊D3)⋊C3)⋊A4 #14518195
Order 1944.
404 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 35 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 | semidirect |
| 2. C3×A4×C3⋊D3 | C3 | semidirect |
| 3. C22×C3×(C3⋊D3)⋊C3 | C3 | semidirect |
| 5. C3×(C3⋊D3)⋊A4 | C3 | semidirect |
| 7. C33×A4 | C2×C3 | semidirect |
| 8. C22×C3×H(3,𝔽3) | C2×C3 | semidirect |
| 14. C3×C22⋊H(3,𝔽3) | D3 | semidirect |
| 15. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 31. C3×(C3⋊D3)⋊C3 | A4 | semidirect |
| 33. C22×C33 | C3×D3 | semidirect |
| 47. C32×A4 | C3×D3 | semidirect |
| 66. C3×H(3,𝔽3) | C2×A4 | semidirect |
| 68. C22×C3⋊D3 | H(3,𝔽3) | semidirect |
| 105. C22×C32 | C2×H(3,𝔽3) | semidirect |
| 134. C3×A4 | (C3⋊D3)⋊C3 | semidirect |
| 145. C33 | D3×A4 | semidirect |
| 179. C3⋊D3 | C22⋊H(3,𝔽3) | semidirect |
| 238. C32 | C2×C22⋊H(3,𝔽3) | semidirect |
| 260. C22 | (C3⋊D3)⋊H(3,𝔽3) | semidirect |
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 |
| C3×A4×C3⋊D3 | 3 |
| C22×C3×(C3⋊D3)⋊C3 | 3 |
| D3×C22⋊H(3,𝔽3) | 3 |
| C3×(C3⋊D3)⋊A4 | 3 |
| (C3⋊D3)⋊H(3,𝔽3) | 4 |