Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
572 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 134 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. C2×C3×C4×C3⋊D3 | C2 | semidirect |
| 3. C33×C4⋊C4 | C2 | semidirect |
| 4. C3×#3752 | C2 | semidirect |
| 5. C3×#3752 | C2 | semidirect |
| 6. C3×#3752 | C2 | semidirect |
| 7. C3×#3750 | C2 | semidirect |
| 8. #64103 | C3 | direct (N × H) |
| 20. C2×C4×C3⋊D3 | C2×C3 | semidirect |
| 24. C32×C4⋊C4 | D3 | semidirect |
| 25. C32×C4⋊C4 | C2×C3 | semidirect |
| 26. #3752 | C2×C3 | semidirect |
| 27. #3752 | C2×C3 | semidirect |
| 28. #3752 | C2×C3 | semidirect |
| 29. #3750 | C2×C3 | semidirect |
| 80. C3×C4⋊C4 | C3×D3 | semidirect |
| 81. C3×C4⋊C4 | C3⋊D3 | semidirect |
| 118. C33 | #123 | semidirect |
| 156. C4⋊C4 | C3×C3⋊D3 | semidirect |
| 189. C32 | #894 | semidirect |
| 190. C32 | C3×#123 | semidirect |
| 226. C3 | C3×#894 | semidirect |
| 227. C3 | #64103 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊(C3⋊D3) | 2 |
| C2×C3×C4×C3⋊D3 | 2 |
| C33×C4⋊C4 | 2 |
| C3×#3752 | 2 |
| C3×#3750 | 2 |
| #64103 | 3 |
| C3×#894 | 3 |