Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
539 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 539 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 17. C8×H(3,𝔽3) | Q8 | semidirect |
| 39. C32×C8 | Dic6 | semidirect |
| 60. H(3,𝔽3) | #498 | semidirect |
| 86. C32 | #4680 | semidirect |
| 91. C8 | #6229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721715 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| #11720550 | 2 |
| C3×#4680 | 3 |