Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
432 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 1. C2×D4×H(3,𝔽3) | C2 | semidirect |
| 2. C2×#638⋊C3 | C2 | semidirect |
| 3. C2×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 4. C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 5. #64149 | C3 | semidirect |
| 15. C2×C32×D4 | D3 | semidirect |
| 16. C2×C32×D4 | C2×C3 | semidirect |
| 17. C2×#638 | C2×C3 | semidirect |
| 18. C2×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 21. C4×C3⋊Dic3 | C2×C3 | semidirect |
| 28. C4×H(3,𝔽3) | D4 | semidirect |
| 29. (C3⋊Dic3)⋊C3 | D4 | semidirect |
| 81. C32×C4 | #67 | semidirect |
| 82. C32×C4 | C3×D4 | semidirect |
| 83. C3⋊Dic3 | C3×D4 | semidirect |
| 86. H(3,𝔽3) | #127 | semidirect |
| 124. C2×D4 | (C3⋊D3)⋊C3 | semidirect |
| 152. C32 | #940 | semidirect |
| 153. C32 | C3×#127 | semidirect |
| 182. C4 | #638⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×H(3,𝔽3) | 2 |
| C2×#638⋊C3 | 2 |
| C2×C4⋊((C3⋊D3)⋊C3) | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| #64149 | 3 |
| C3×#940 | 3 |