Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
319 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 75 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. H(3,𝔽3)×M32 | C2 | semidirect |
| 3. #11720550 | C2 | semidirect |
| 8. #88530 | C4 | semidirect |
| 9. #88529 | C4 | semidirect |
| 13. C32×M32 | D3 | semidirect |
| 77. M32 | #272 | semidirect |
| 79. H(3,𝔽3) | #360 | semidirect |
| 118. C32 | #4518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721779 | 2 |
| H(3,𝔽3)×M32 | 2 |
| #11720550 | 2 |
| C3×#4518 | 3 |