Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
684 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 198 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. C22×C33×C4 | C2 | semidirect |
| 3. C32×#217 | C2 | semidirect |
| 4. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C32×Dic3⋊C4 | C2 | semidirect |
| 7. C3×#929 | C3 | direct (N × H) |
| 17. C22×C32×C4 | D3 | semidirect |
| 18. C22×C32×C4 | C2×C3 | semidirect |
| 23. C3×#217 | C2×C3 | semidirect |
| 24. C3×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 25. C3×Dic3⋊C4 | C2×C3 | semidirect |
| 35. #929 | C32 | direct (N × H) |
| 59. C22×C3×C4 | C3×D3 | semidirect |
| 60. C22×C3×C4 | C2×C32 | semidirect |
| 65. #217 | C2×C32 | semidirect |
| 66. (C2×D3)⋊C4 | C2×C32 | semidirect |
| 67. Dic3⋊C4 | C2×C32 | semidirect |
| 89. C33 | #123 | semidirect |
| 119. C22×C4 | C32×D3 | semidirect |
| 144. C32 | #929 | direct (N × H) |
| 145. C32 | C3×#123 | semidirect |
| 173. C3 | C3×#929 | direct (N × H) |
| 174. C3 | C32×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×C4 | 2 |
| C2×C32×#67 | 2 |
| C32×#217 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| C32×Dic3⋊C4 | 2 |
| C32×#123 | 3 |
| C3×#929 | 3 |