Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
512 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 130 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. C3×#3756 | C2 | semidirect |
| 4. C3×#3755 | C2 | semidirect |
| 5. C3×#3748 | C2 | semidirect |
| 6. #64151 | C3 | direct (N × H) |
| 18. C2×C32×Q8 | D3 | semidirect |
| 19. C2×C32×Q8 | C2×C3 | semidirect |
| 22. #3756 | C2×C3 | semidirect |
| 23. #3755 | C2×C3 | semidirect |
| 24. #3748 | C2×C3 | semidirect |
| 63. C2×C3×Q8 | C3×D3 | semidirect |
| 64. C2×C3×Q8 | C3⋊D3 | semidirect |
| 89. C33 | #137 | semidirect |
| 121. C2×Q8 | C3×C3⋊D3 | semidirect |
| 142. C32 | #942 | semidirect |
| 143. C32 | C3×#137 | semidirect |
| 168. C3 | C3×#942 | semidirect |
| 169. C3 | #64151 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q8 | 2 |
| C3×#3828 | 2 |
| C3×#3756 | 2 |
| C3×#3755 | 2 |
| C3×#3748 | 2 |
| #64151 | 3 |
| C3×#942 | 3 |