Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
625 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 625 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 3. C32×#627 | C3 | semidirect |
| 13. C32×H(3,𝔽3) | Q8 | semidirect |
| 36. C34 | C3×Q8 | semidirect |
| 40. C3×H(3,𝔽3) | Dic6 | semidirect |
| 44. #627 | H(3,𝔽3) | direct (N × H) |
| 79. C33 | C3×Dic6 | semidirect |
| 84. H(3,𝔽3) | #627 | direct (N × H) |
| 127. C32 | Q8×H(3,𝔽3) | semidirect |
| 128. C32 | C3×#627 | semidirect |
| 147. C3 | Dic6×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×C3⋊Dic3 | 2 |
| C3×Dic3×H(3,𝔽3) | 2 |
| C32×#627 | 3 |
| Dic6×H(3,𝔽3) | 3 |