Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
780 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 210 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×C32×#67 | C2 | semidirect |
| 3. C2×C32×C4×D3 | C2 | semidirect |
| 4. C32×#217 | C2 | semidirect |
| 5. C32×C4⋊Dic3 | C2 | semidirect |
| 7. C3×#938 | C3 | direct (N × H) |
| 18. C2×C32×D4 | D3 | semidirect |
| 19. C2×C32×D4 | C2×C3 | semidirect |
| 21. C2×C3×#67 | C2×C3 | semidirect |
| 22. C2×C3×C4×D3 | C2×C3 | semidirect |
| 25. C3×#217 | C2×C3 | semidirect |
| 26. C3×C4⋊Dic3 | C2×C3 | semidirect |
| 33. C2×C32×D3 | D4 | semidirect |
| 34. C33×C4 | D4 | semidirect |
| 38. #938 | C32 | direct (N × H) |
| 65. C2×C3×D4 | C3×D3 | semidirect |
| 66. C2×C3×D4 | C2×C32 | semidirect |
| 68. C2×#67 | C2×C32 | semidirect |
| 69. C2×C4×D3 | C2×C32 | semidirect |
| 72. #217 | C2×C32 | semidirect |
| 73. C4⋊Dic3 | C2×C32 | semidirect |
| 91. C2×C3×D3 | C3×D4 | semidirect |
| 95. C32×C4 | #67 | semidirect |
| 96. C32×C4 | C3×D4 | semidirect |
| 100. C33 | #121 | semidirect |
| 135. C2×D4 | C32×D3 | semidirect |
| 156. C2×D3 | C32×D4 | semidirect |
| 160. C3×C4 | C3×#67 | semidirect |
| 161. C3×C4 | C32×D4 | semidirect |
| 165. C32 | #938 | direct (N × H) |
| 166. C32 | C3×#121 | semidirect |
| 198. C4 | C32×#67 | semidirect |
| 200. C3 | C3×#938 | direct (N × H) |
| 201. C3 | C32×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×D4 | 2 |
| C2×C32×#67 | 2 |
| C2×C32×C4×D3 | 2 |
| C32×#217 | 2 |
| C32×C4⋊Dic3 | 2 |
| C32×#121 | 3 |
| C3×#938 | 3 |