Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
297 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 297 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 14. C8×H(3,𝔽3) | C8 | semidirect |
| 35. C32×C8 | C3⋊C8 | semidirect |
| 56. H(3,𝔽3) | #334 | semidirect |
| 86. C32 | #4457 | semidirect |
| 92. C8 | #6180 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×H(3,𝔽3) | 2 |
| C4⋊#6180 | 2 |
| C3×#4457 | 3 |