Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
389 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 389 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 |
|---|---|---|
| 1. (C3×A4)⋊H(3,𝔽3) | C2 | semidirect |
| 2. C32×C3⋊S4 | C3 | semidirect |
| 3. C3×(C3⋊S4)⋊C3 | C3 | semidirect |
| 6. C33×A4 | C2×C3 | semidirect |
| 7. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 11. C3×C22⋊H(3,𝔽3) | C2×C3 | semidirect |
| 26. C22×C33 | C3×D3 | semidirect |
| 52. C3×H(3,𝔽3) | S4 | semidirect |
| 53. C3⋊S4 | H(3,𝔽3) | semidirect |
| 81. C22×C32 | (C3⋊D3)⋊C3 | semidirect |
| 101. C3×A4 | C2×H(3,𝔽3) | semidirect |
| 116. C33 | C3×S4 | semidirect |
| 186. C32 | (C3⋊S4)⋊C3 | semidirect |
| 202. 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 |
| C32×C3⋊S4 | 3 |
| C3×(C3⋊S4)⋊C3 | 3 |
| #67×H(3,𝔽3) | 3 |
| (C3⋊D3)⋊H(3,𝔽3) | 4 |