Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
228 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 65 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. Q16×H(3,𝔽3) | C2 | semidirect |
| 3. #3756⋊C3 | C2 | semidirect |
| 5. #3746⋊C3 | C2 | semidirect |
| 6. Q16×C3⋊D3 | C3 | semidirect |
| 18. C32×Q16 | D3 | semidirect |
| 19. C32×Q16 | C2×C3 | semidirect |
| 20. #3756 | C2×C3 | semidirect |
| 21. #3746 | C2×C3 | semidirect |
| 51. (C3⋊D3)⋊C3 | Q16 | direct (N × H) |
| 81. H(3,𝔽3) | C2×Q16 | semidirect |
| 108. C3⋊D3 | C3×Q16 | semidirect |
| 113. Q16 | (C3⋊D3)⋊C3 | direct (N × H) |
| 133. C32 | D3×Q16 | semidirect |
| 134. C32 | C2×C3×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×(C3⋊D3)⋊C3 | 2 |
| Q16×H(3,𝔽3) | 2 |
| #3756⋊C3 | 2 |
| C8×(C3⋊D3)⋊C3 | 2 |
| #3746⋊C3 | 2 |
| Q16×C3⋊D3 | 3 |
| C3×D3×Q16 | 3 |