Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
257 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 257 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. #41×H(3,𝔽3) | C2 | semidirect |
| 2. #3828⋊C3 | C2 | semidirect |
| 3. #3755⋊C3 | C2 | semidirect |
| 4. #3756⋊C3 | C2 | semidirect |
| 5. #3753⋊C3 | C2 | semidirect |
| 6. #3754⋊C3 | C2 | semidirect |
| 7. C2×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 8. #64159 | C3 | semidirect |
| 22. C32×#41 | D3 | semidirect |
| 23. C32×#41 | C2×C3 | semidirect |
| 24. #3828 | C2×C3 | semidirect |
| 26. #3756 | C2×C3 | semidirect |
| 27. #3755 | C2×C3 | semidirect |
| 28. #3754 | C2×C3 | semidirect |
| 29. #3753 | C2×C3 | semidirect |
| 30. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 119. H(3,𝔽3) | #135 | semidirect |
| 170. #41 | (C3⋊D3)⋊C3 | semidirect |
| 203. C32 | #950 | semidirect |
| 204. C32 | C3×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×H(3,𝔽3) | 2 |
| #3828⋊C3 | 2 |
| #3755⋊C3 | 2 |
| #3756⋊C3 | 2 |
| #3753⋊C3 | 2 |
| #3754⋊C3 | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| #64159 | 3 |
| C3×#950 | 3 |