Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
825 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 825 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 4. #11720583 | C2 | semidirect |
| 8. C2×Q8×H(3,𝔽3) | C4 | semidirect |
| 37. C2×C32×Q8 | Dic3 | semidirect |
| 112. H(3,𝔽3) | #419 | semidirect |
| 142. C2×Q8 | #1084 | semidirect |
| 167. C32 | #5225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×H(3,𝔽3) | 2 |
| #11721826 | 2 |
| C2×#88538 | 2 |
| #11720583 | 2 |
| C3×#5225 | 3 |