Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
600 conjugacy classes of subgroups; only the 132 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 132 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 |
| 4. C2×#6196 | C2 | semidirect |
| 5. #88651 | C2 | direct (N × H) |
| 12. #634⋊C3 | C22 | semidirect |
| 14. #6196 | C22 | semidirect |
| 15. C2×#634 | D3 | semidirect |
| 23. C2×#272 | Q8 | semidirect |
| 35. #634 | C2×D3 | semidirect |
| 44. C2×H(3,𝔽3) | C2×Q8 | semidirect |
| 46. #272 | C2×Q8 | semidirect |
| 72. H(3,𝔽3) | C22×Q8 | semidirect |
| 97. C2×C32 | D3×Q8 | semidirect |
| 125. C32 | C2×D3×Q8 | semidirect |
| 153. C2 | #88651 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#272 | 2 |
| C2×#634⋊C3 | 2 |
| C2×#6199 | 2 |
| C2×#6196 | 2 |
| #88651 | 2 |
| C2×D3×Dic6 | 3 |