Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
258 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 67 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. #3828⋊C3 | C2 | semidirect |
| 2. C2×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. M16×H(3,𝔽3) | C2 | semidirect |
| 4. #3745⋊C3 | C2 | semidirect |
| 5. #3744⋊C3 | C2 | semidirect |
| 6. #64117 | C3 | semidirect |
| 13. C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 15. #634⋊C3 | C22 | semidirect |
| 16. C8×H(3,𝔽3) | C22 | semidirect |
| 17. #3828 | C2×C3 | semidirect |
| 18. C2×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 22. C32×M16 | D3 | semidirect |
| 23. C32×M16 | C2×C3 | semidirect |
| 24. #3745 | C2×C3 | semidirect |
| 25. #3744 | C2×C3 | semidirect |
| 46. C4⋊(C3⋊D3) | C22×C3 | semidirect |
| 48. #634 | C22×C3 | semidirect |
| 56. C32×C8 | C2×D3 | semidirect |
| 57. C32×C8 | C22×C3 | semidirect |
| 96. H(3,𝔽3) | AGL(1,ℤ/8) | semidirect |
| 140. M16 | (C3⋊D3)⋊C3 | semidirect |
| 166. C32 | #908 | semidirect |
| 167. C32 | C3×AGL(1,ℤ/8) | semidirect |
| 176. 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 |
|---|---|
| #3828⋊C3 | 2 |
| C2×C4⋊((C3⋊D3)⋊C3) | 2 |
| M16×H(3,𝔽3) | 2 |
| #3745⋊C3 | 2 |
| #3744⋊C3 | 2 |
| #64117 | 3 |
| C3×#908 | 3 |