Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
847 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 847 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 12. C4×#1084 | C4 | semidirect |
| 98. H(3,𝔽3) | #382 | semidirect |
| 151. C32 | #4977 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×H(3,𝔽3) | 2 |
| C2×C4⋊#1084 | 2 |
| C2×C4×#1084 | 2 |
| #11720574 | 2 |
| C3×#4977 | 3 |