Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
627 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 627 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 4. #11720530 | C2 | semidirect |
| 5. #11720529 | C2 | semidirect |
| 14. C2×#6180 | C4 | semidirect |
| 107. H(3,𝔽3) | #427 | semidirect |
| 155. C32 | #4998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#117 | 2 |
| #11721826 | 2 |
| C22×#6180 | 2 |
| #11720530 | 2 |
| #11720529 | 2 |
| C3×#4998 | 3 |