Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
240 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 67 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. C42×H(3,𝔽3) | C2 | semidirect |
| 3. #3750⋊C3 | C2 | semidirect |
| 4. #64085 | C3 | semidirect |
| 10. C32×C42 | D3 | semidirect |
| 11. C32×C42 | C2×C3 | semidirect |
| 13. #3750 | C2×C3 | semidirect |
| 53. H(3,𝔽3) | #126 | semidirect |
| 71. C42 | (C3⋊D3)⋊C3 | semidirect |
| 87. C32 | #876 | semidirect |
| 88. C32 | C3×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×H(3,𝔽3) | 2 |
| #3752⋊C3 | 2 |
| #3750⋊C3 | 2 |
| #64085 | 3 |
| C3×#876 | 3 |