Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
248 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 3. #3756⋊C3 | C2 | direct (N × H) |
| 5. C2×#3756 | C3 | semidirect |
| 20. #3756 | C2×C3 | semidirect |
| 52. C2×H(3,𝔽3) | Q16 | semidirect |
| 82. H(3,𝔽3) | C2×Q16 | semidirect |
| 113. C2×C32 | #216 | semidirect |
| 114. C2×C32 | C3×Q16 | semidirect |
| 141. C32 | C2×#216 | semidirect |
| 142. C32 | C2×C3×Q16 | semidirect |
| 168. C2 | #3756⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×H(3,𝔽3) | 2 |
| C2×#634⋊C3 | 2 |
| #3756⋊C3 | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C2×#3756 | 3 |
| C2×C3×#216 | 3 |