Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
293 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 293 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 10. Q8×H(3,𝔽3) | C8 | semidirect |
| 15. #6188 | Q8 | direct (N × H) |
| 53. H(3,𝔽3) | C8×Q8 | semidirect |
| 83. Q8 | #6188 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#1084 | 2 |
| C4⋊#6188 | 2 |
| C4×#6188 | 2 |
| C3×C8×Q8 | 9 |