Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
528 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 29. #6229 | Q8 | semidirect |
| 105. H(3,𝔽3) | #475 | semidirect |
| 154. C32 | #4851 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721715 | 2 |
| C4×#6229 | 2 |
| H(3,𝔽3)×C4⋊C8 | 2 |
| #11720550 | 2 |
| #11720549 | 2 |
| C3×#4851 | 3 |