Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
869 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 869 conjugacy classes of subgroups — too many to draw. Only its 221 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. C2×#88538 | C2 | semidirect |
| 3. C22×#6180 | C2 | semidirect |
| 4. #11720573 | C2 | semidirect |
| 119. H(3,𝔽3) | #408 | semidirect |
| 181. C32 | #5234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×H(3,𝔽3) | 2 |
| C2×#88538 | 2 |
| C22×#6180 | 2 |
| #11720573 | 2 |
| C3×#5234 | 3 |