Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
627 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 627 conjugacy classes of subgroups — too many to draw. Only its 217 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 |
|---|---|---|
| 7. C2×C8×H(3,𝔽3) | C4 | semidirect |
| 9. C4⋊#1084 | C4 | semidirect |
| 26. C2×C32×C8 | Dic3 | semidirect |
| 80. H(3,𝔽3) | #340 | semidirect |
| 107. C2×C8 | #1084 | semidirect |
| 128. C32 | #4551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×H(3,𝔽3) | 2 |
| C2×C4⋊#1084 | 2 |
| C3×#4551 | 3 |