Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1023 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 1023 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. #11720579 | C2 | direct (N × H) |
| 12. #88538 | C22 | semidirect |
| 72. C2×H(3,𝔽3) | #100 | semidirect |
| 105. H(3,𝔽3) | C2×#100 | semidirect |
| 133. C2×C32 | #833 | semidirect |
| 164. C32 | C2×#833 | semidirect |
| 202. C2 | #11720579 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×H(3,𝔽3) | 2 |
| C2×#88538 | 2 |
| #11720579 | 2 |
| C2×C3×#833 | 3 |