Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
292 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 292 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. #3754⋊C3 | C2 | direct (N × H) |
| 4. C2×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 5. C2×#3754 | C3 | semidirect |
| 13. #634⋊C3 | C22 | semidirect |
| 14. (C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 18. C2×#634 | C2×C3 | semidirect |
| 20. #3754 | C2×C3 | semidirect |
| 21. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 47. #634 | C22×C3 | semidirect |
| 51. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 54. C2×H(3,𝔽3) | SD16 | semidirect |
| 87. H(3,𝔽3) | C2×SD16 | semidirect |
| 121. C2×C32 | #214 | semidirect |
| 122. C2×C32 | C3×SD16 | semidirect |
| 153. C32 | C2×#214 | semidirect |
| 154. C32 | C2×C3×SD16 | semidirect |
| 186. C2 | #3754⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×H(3,𝔽3) | 2 |
| C2×#634⋊C3 | 2 |
| #3754⋊C3 | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C2×#3754 | 3 |
| C2×C3×#214 | 3 |