Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
228 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 61 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. Q8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. Q16×H(3,𝔽3) | C2 | semidirect |
| 4. #3755⋊C3 | C2 | semidirect |
| 5. #3756⋊C3 | C2 | semidirect |
| 6. #3744⋊C3 | C2 | semidirect |
| 7. #3743⋊C3 | C2 | semidirect |
| 8. #64127 | C3 | semidirect |
| 22. Q8×C3⋊D3 | C2×C3 | semidirect |
| 26. C32×Q16 | D3 | semidirect |
| 27. C32×Q16 | C2×C3 | semidirect |
| 28. #3756 | C2×C3 | semidirect |
| 29. #3755 | C2×C3 | semidirect |
| 30. #3744 | C2×C3 | semidirect |
| 31. #3743 | C2×C3 | semidirect |
| 114. H(3,𝔽3) | #137 | semidirect |
| 161. Q16 | (C3⋊D3)⋊C3 | semidirect |
| 190. C32 | #918 | semidirect |
| 191. C32 | C3×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88722 | 2 |
| Q8×(C3⋊D3)⋊C3 | 2 |
| Q16×H(3,𝔽3) | 2 |
| #3755⋊C3 | 2 |
| #3756⋊C3 | 2 |
| #3744⋊C3 | 2 |
| #3743⋊C3 | 2 |
| #64127 | 3 |
| C3×#918 | 3 |