Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
319 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 9. #88530 | C4 | semidirect |
| 71. H(3,𝔽3) | #358 | semidirect |
| 105. C32 | #4503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88530 | 2 |
| C2×C16×H(3,𝔽3) | 2 |
| #11720551 | 2 |
| C3×#4503 | 3 |