Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
287 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 287 conjugacy classes of subgroups — too many to draw. Only its 79 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. #11720779 | C2 | direct (N × H) |
| 3. C2×#88410 | C2 | semidirect |
| 9. #88410 | C22 | semidirect |
| 45. C2×H(3,𝔽3) | M32 | semidirect |
| 67. H(3,𝔽3) | C2×M32 | semidirect |
| 129. C2 | #11720779 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6180 | 2 |
| #11720779 | 2 |
| C2×#88410 | 2 |
| C2×C3×M32 | 9 |