Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
359 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 359 conjugacy classes of subgroups — too many to draw. Only its 56 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. Q8×#634 | C3 | semidirect |
| 18. Q8⋊H(3,𝔽3) | Q8 | semidirect |
| 51. C32×Q8 | C3×Q8 | semidirect |
| 60. #634 | SL(2,𝔽3) | semidirect |
| 64. C3×SL(2,𝔽3) | Dic6 | semidirect |
| 171. C32 | Q8×SL(2,𝔽3) | semidirect |
| 175. Q8 | #634⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8⋊H(3,𝔽3) | 2 |
| #11720765 | 2 |
| Q8×#634 | 3 |
| SL(2,𝔽3)×Dic6 | 3 |
| C2×#634⋊C3 | 4 |