Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
264 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 60 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. C22×C32×Q8 | C3 | semidirect |
| 3. C3×Q8×A4 | C3 | semidirect |
| 10. C22⋊H(3,𝔽3) | Q8 | direct (N × H) |
| 20. C32×Q8 | A4 | semidirect |
| 33. C22×C32 | C3×Q8 | semidirect |
| 34. C3×A4 | C3×Q8 | semidirect |
| 38. C22×Q8 | H(3,𝔽3) | semidirect |
| 74. C32 | Q8×A4 | semidirect |
| 78. Q8 | C22⋊H(3,𝔽3) | direct (N × H) |
| 90. C22 | Q8×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C22⋊H(3,𝔽3) | 2 |
| C22×C32×Q8 | 3 |
| C3×Q8×A4 | 3 |
| Q8×H(3,𝔽3) | 4 |