Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
197 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 46 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. C32×Q8⋊C9 | C3 | semidirect |
| 3. #10619584 | C3 | semidirect |
| 10. Q8×H(3,𝔽3) | C9 | semidirect |
| 56. H(3,𝔽3) | Q8⋊C9 | semidirect |
| 98. Q8 | H(3,𝔽3)⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×H(3,𝔽3) | 3 |
| C32×Q8⋊C9 | 3 |
| #10619584 | 3 |
| C2×H(3,𝔽3)⋊C9 | 4 |