Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1199 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1199 conjugacy classes of subgroups — too many to draw. Only its 277 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 |
|---|---|---|
| 3. #11720574 | C2 | semidirect |
| 7. C22×C4×H(3,𝔽3) | C4 | semidirect |
| 27. C22×C32×C4 | Dic3 | semidirect |
| 82. H(3,𝔽3) | #381 | semidirect |
| 108. C22×C4 | #1084 | semidirect |
| 127. C32 | #5211 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×H(3,𝔽3) | 2 |
| C2×#88552 | 2 |
| #11720574 | 2 |
| C3×#5211 | 3 |