Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
197 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 197 conjugacy classes of subgroups — too many to draw. Only its 50 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×#6180 | C2 | semidirect |
| 3. C4⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 10. C4⋊((C3⋊D3)⋊C3) | C4 | semidirect |
| 14. C4⋊(C3⋊Dic3) | D3 | semidirect |
| 36. C4⋊(C3⋊D3) | Dic3 | semidirect |
| 75. H(3,𝔽3) | #102 | semidirect |
| 135. C32 | #809 | semidirect |
| 136. C32 | #832 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊((C3⋊D3)⋊C3) | 2 |
| C2×#6180 | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| #63564 | 3 |
| #63563 | 3 |