Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
299 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 299 conjugacy classes of subgroups — too many to draw. Only its 71 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×#88410 | C2 | semidirect |
| 3. #11720770 | C2 | direct (N × H) |
| 9. #88410 | C22 | semidirect |
| 26. C2×#272 | C16 | semidirect |
| 44. C2×H(3,𝔽3) | C2×C16 | semidirect |
| 46. #272 | C2×C16 | semidirect |
| 67. H(3,𝔽3) | C22×C16 | semidirect |
| 129. C2 | #11720770 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#272 | 2 |
| C2×#88410 | 2 |
| #11720770 | 2 |
| C22×C3×C16 | 9 |