Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
307 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 60 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. C22×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 3. #88552 | C2 | semidirect |
| 4. #88450 | C2 | semidirect |
| 5. #88449 | C2 | semidirect |
| 16. C22×C3⋊Dic3 | D3 | semidirect |
| 94. H(3,𝔽3) | #123 | semidirect |
| 163. C32 | #929 | semidirect |
| 164. C32 | #935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#638⋊C3 | 2 |
| C22×(C3⋊Dic3)⋊C3 | 2 |
| #88552 | 2 |
| #88450 | 2 |
| #88449 | 2 |
| #63966 | 3 |
| #63962 | 3 |