Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
495 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 28. #6180 | Q8 | semidirect |
| 99. H(3,𝔽3) | #501 | semidirect |
| 142. C32 | #5064 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#125 | 2 |
| #11721715 | 2 |
| #11720530 | 2 |
| #11720529 | 2 |
| #11720520 | 2 |
| C3×#5064 | 3 |