Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
153 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 153 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 2. C2×#88586 | C2 | semidirect |
| 19. C22×H(3,𝔽3) | C16 | semidirect |
| 51. H(3,𝔽3) | C22⋊C16 | semidirect |
| 105. C22 | #88586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6188 | 2 |
| C2×#88586 | 2 |
| #4549 | 9 |