Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
612 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 116 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. Q8×#272 | C2 | semidirect |
| 2. #88722 | C2 | semidirect |
| 3. #88655 | C2 | semidirect |
| 4. C4×((C3⋊D3)⋊C3)⋊C2 | C2 | semidirect |
| 5. #88648 | C2 | semidirect |
| 8. Q8×H(3,𝔽3) | C22 | semidirect |
| 10. #6229 | C22 | semidirect |
| 11. C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 12. C4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 14. #6198 | C22 | semidirect |
| 15. ((C3⋊D3)⋊C3)⋊C4 | C22 | semidirect |
| 16. #3832 | D3 | semidirect |
| 34. C32×Q8 | C2×D3 | semidirect |
| 35. C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 36. C4×C3⋊D3 | C2×D3 | semidirect |
| 48. #272 | #41 | semidirect |
| 75. H(3,𝔽3) | C2×#41 | semidirect |
| 129. C32 | D3×#41 | semidirect |
| 132. Q8 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#272 | 2 |
| #88722 | 2 |
| #88655 | 2 |
| C4×((C3⋊D3)⋊C3)⋊C2 | 2 |
| #88648 | 2 |
| D3×#239 | 3 |