Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1023 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 1023 conjugacy classes of subgroups — too many to draw. Only its 257 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. C2×#6229 | C4 | semidirect |
| 25. C2×C4×H(3,𝔽3) | Q8 | semidirect |
| 63. C2×C32×C4 | Dic6 | semidirect |
| 110. H(3,𝔽3) | #391 | semidirect |
| 169. C32 | #4929 | semidirect |
| 179. C2×C4 | #6229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6229 | 2 |
| C2×C42×H(3,𝔽3) | 2 |
| C2×C4⋊#1084 | 2 |
| #11720574 | 2 |
| C3×#4929 | 3 |