Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
288 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 288 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 |
|---|---|---|
| 1. D4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 2. D8×H(3,𝔽3) | C2 | semidirect |
| 3. #3753⋊C3 | C2 | semidirect |
| 4. #3745⋊C3 | C2 | semidirect |
| 5. C8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 6. D8×C3⋊D3 | C3 | semidirect |
| 9. D4×H(3,𝔽3) | C22 | semidirect |
| 11. C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 13. C8×H(3,𝔽3) | C22 | semidirect |
| 14. (C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 15. D4×C3⋊D3 | C2×C3 | semidirect |
| 18. C32×D8 | D3 | semidirect |
| 19. C32×D8 | C2×C3 | semidirect |
| 20. #3753 | C2×C3 | semidirect |
| 21. #3745 | C2×C3 | semidirect |
| 22. C8×C3⋊D3 | C2×C3 | semidirect |
| 38. C32×D4 | C2×D3 | semidirect |
| 39. C32×D4 | C22×C3 | semidirect |
| 41. C4⋊(C3⋊D3) | C22×C3 | semidirect |
| 47. C32×C8 | C2×D3 | semidirect |
| 48. C32×C8 | C22×C3 | semidirect |
| 49. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 54. (C3⋊D3)⋊C3 | D8 | direct (N × H) |
| 86. H(3,𝔽3) | C2×D8 | semidirect |
| 117. C3⋊D3 | C3×D8 | semidirect |
| 123. D8 | (C3⋊D3)⋊C3 | direct (N × H) |
| 146. C32 | D3×D8 | semidirect |
| 147. C32 | C2×C3×D8 | semidirect |
| 151. D4 | C2×(C3⋊D3)⋊C3 | semidirect |
| 154. C8 | C2×(C3⋊D3)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×(C3⋊D3)⋊C3 | 2 |
| D8×H(3,𝔽3) | 2 |
| #3753⋊C3 | 2 |
| #3745⋊C3 | 2 |
| C8×(C3⋊D3)⋊C3 | 2 |
| D8×C3⋊D3 | 3 |
| C3×D3×D8 | 3 |