Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
671 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 671 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
|---|---|---|
| 26. C4×H(3,𝔽3) | Q16 | semidirect |
| 54. C32×C4 | Dic12 | semidirect |
| 60. H(3,𝔽3) | #494 | semidirect |
| 86. C32 | #4699 | semidirect |
| 98. C4 | #88530 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88530 | 2 |
| #11721715 | 2 |
| C4×C8×H(3,𝔽3) | 2 |
| C3×#4699 | 3 |