Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
513 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
|---|---|---|
| 4. #10619956 | C3 | semidirect |
| 11. C32⋊H(3,𝔽3) | Q8 | semidirect |
| 12. #6308 | C32 | semidirect |
| 32. C34 | Dic6 | semidirect |
| 34. C3×H(3,𝔽3) | C3×Q8 | semidirect |
| 69. C33 | C32×Q8 | semidirect |
| 105. C32 | #634⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C32⋊H(3,𝔽3) | 2 |
| #11757562 | 2 |
| C32×#634 | 3 |
| #10619956 | 3 |