Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
550 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 550 conjugacy classes of subgroups — too many to draw. Only its 109 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. #11721715 | C2 | semidirect |
| 3. #11720583 | C2 | semidirect |
| 5. #11720520 | C2 | semidirect |
| 108. H(3,𝔽3) | #489 | semidirect |
| 160. C32 | #5055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#124 | 2 |
| #11721715 | 2 |
| #11720583 | 2 |
| #11720578 | 2 |
| #11720520 | 2 |
| C3×#5055 | 3 |