Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
229 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 229 conjugacy classes of subgroups — too many to draw. Only its 48 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. C4⋊((C3⋊Dic3)⋊C3) | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 9. C4⋊#272 | C4 | semidirect |
| 15. C4⋊(C3⋊Dic3) | D3 | semidirect |
| 16. C2×C3⋊(C3⋊C8) | D3 | semidirect |
| 80. H(3,𝔽3) | #102 | semidirect |
| 146. C32 | #809 | semidirect |
| 147. C32 | #821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#272 | 2 |
| C4⋊((C3⋊Dic3)⋊C3) | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #63563 | 3 |
| #63562 | 3 |