Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
260 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×#634⋊C3 | C2 | semidirect |
| 3. C2×C8×H(3,𝔽3) | C2 | semidirect |
| 4. #3744⋊C3 | C2 | direct (N × H) |
| 5. C2×#3744 | C3 | semidirect |
| 13. #634⋊C3 | C22 | semidirect |
| 14. C8×H(3,𝔽3) | C22 | semidirect |
| 16. C2×#634 | C2×C3 | semidirect |
| 20. C2×C32×C8 | D3 | semidirect |
| 21. C2×C32×C8 | C2×C3 | semidirect |
| 22. #3744 | C2×C3 | semidirect |
| 42. #634 | C22×C3 | semidirect |
| 49. C32×C8 | C2×D3 | semidirect |
| 50. C32×C8 | C22×C3 | semidirect |
| 51. C2×H(3,𝔽3) | SD16 | semidirect |
| 83. H(3,𝔽3) | C2×SD16 | semidirect |
| 112. C2×C32 | #204 | semidirect |
| 113. C2×C32 | C3×SD16 | semidirect |
| 121. C2×C8 | (C3⋊D3)⋊C3 | semidirect |
| 144. C32 | C2×#204 | semidirect |
| 145. C32 | C2×C3×SD16 | semidirect |
| 153. C8 | C2×(C3⋊D3)⋊C3 | semidirect |
| 176. C2 | #3744⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊((C3⋊D3)⋊C3) | 2 |
| C2×#634⋊C3 | 2 |
| C2×C8×H(3,𝔽3) | 2 |
| #3744⋊C3 | 2 |
| C2×#3744 | 3 |
| C2×C3×#204 | 3 |