Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
780 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 158 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. C2×C33×D4 | C2 | semidirect |
| 2. C2×C3×#638 | C2 | semidirect |
| 3. C2×C3×#638 | C2 | semidirect |
| 4. C22×C3×C3⋊Dic3 | C2 | semidirect |
| 5. C3×#3757 | C2 | semidirect |
| 6. C3×#3752 | C2 | semidirect |
| 7. C3×#3750 | C2 | semidirect |
| 8. #64148 | C3 | direct (N × H) |
| 22. C2×C32×D4 | D3 | semidirect |
| 23. C2×C32×D4 | C2×C3 | semidirect |
| 24. C2×#638 | C2×C3 | semidirect |
| 25. C2×#638 | C2×C3 | semidirect |
| 26. C22×C3⋊Dic3 | C2×C3 | semidirect |
| 30. #3757 | C2×C3 | semidirect |
| 31. #3752 | C2×C3 | semidirect |
| 32. #3750 | C2×C3 | semidirect |
| 41. C22×C33 | D4 | semidirect |
| 49. C3×C3⋊Dic3 | D4 | semidirect |
| 87. C2×C3×D4 | C3×D3 | semidirect |
| 88. C2×C3×D4 | C3⋊D3 | semidirect |
| 116. C22×C32 | #67 | semidirect |
| 117. C22×C32 | C3×D4 | semidirect |
| 131. C3⋊Dic3 | C3×D4 | semidirect |
| 136. C33 | #121 | semidirect |
| 182. C2×D4 | C3×C3⋊D3 | semidirect |
| 207. C22×C3 | C3×#67 | semidirect |
| 208. C22×C3 | #638 | semidirect |
| 224. C32 | #939 | semidirect |
| 225. C32 | C3×#121 | semidirect |
| 262. C22 | C3×#638 | semidirect |
| 269. C3 | C3×#939 | semidirect |
| 270. C3 | #64148 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D4 | 2 |
| C2×C3×#638 | 2 |
| C22×C3×C3⋊Dic3 | 2 |
| C3×#3757 | 2 |
| C3×#3752 | 2 |
| C3×#3750 | 2 |
| #64148 | 3 |
| C3×#939 | 3 |