Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
287 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 287 conjugacy classes of subgroups — too many to draw. Only its 59 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 | semidirect |
| 3. #11720771 | C2 | semidirect |
| 4. #11720770 | C2 | semidirect |
| 12. #88410 | C22 | semidirect |
| 61. #272 | M32 | semidirect |
| 89. H(3,𝔽3) | C2×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×#272 | 2 |
| #11720779 | 2 |
| #11720771 | 2 |
| #11720770 | 2 |
| C2×C3×M32 | 9 |