Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
825 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 825 conjugacy classes of subgroups — too many to draw. Only its 207 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. #11720584 | C2 | semidirect |
| 4. #11720579 | C2 | semidirect |
| 113. H(3,𝔽3) | #413 | semidirect |
| 172. C32 | #5237 | 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 |
| #11720584 | 2 |
| #11720579 | 2 |
| C3×#5237 | 3 |