Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
608 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 198 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×C33×Q8 | C2 | semidirect |
| 3. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 4. C32×C4×Dic3 | C2 | semidirect |
| 6. C3×#947 | C3 | direct (N × H) |
| 14. C2×C32×Q8 | D3 | semidirect |
| 15. C2×C32×Q8 | C2×C3 | semidirect |
| 20. C3×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 21. C3×C4×Dic3 | C2×C3 | semidirect |
| 29. #947 | C32 | direct (N × H) |
| 49. C2×C3×Q8 | C3×D3 | semidirect |
| 50. C2×C3×Q8 | C2×C32 | semidirect |
| 55. (C2×D3)⋊C4 | C2×C32 | semidirect |
| 56. C4×Dic3 | C2×C32 | semidirect |
| 73. C33 | #124 | semidirect |
| 97. C2×Q8 | C32×D3 | semidirect |
| 117. C32 | #947 | direct (N × H) |
| 118. C32 | C3×#124 | semidirect |
| 140. C3 | C3×#947 | direct (N × H) |
| 141. C3 | C32×#124 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q8 | 2 |
| C2×C32×D12 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| C32×C4×Dic3 | 2 |
| C32×#124 | 3 |
| C3×#947 | 3 |