Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
411 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 411 conjugacy classes of subgroups — too many to draw. Only its 38 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. C3⋊#6188 | C3 | direct (N × H) |
| 9. C32×H(3,𝔽3) | C8 | semidirect |
| 31. C3×H(3,𝔽3) | C3⋊C8 | semidirect |
| 32. C3×H(3,𝔽3) | C3×C8 | semidirect |
| 75. H(3,𝔽3) | C3×C3⋊C8 | semidirect |
| 116. C32 | #6188 | semidirect |
| 136. C3 | C3×#6188 | semidirect |
| 137. C3 | C3⋊#6188 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#1084 | 2 |
| C3⋊#6188 | 3 |
| C3×#6188 | 3 |
| C32×C3⋊C8 | 9 |