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×C4×C3⋊D3 | C2 | semidirect |
| 4. C3×#3757 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 6. #64147 | C3 | direct (N × H) |
| 17. C2×C32×D4 | D3 | semidirect |
| 18. C2×C32×D4 | C2×C3 | semidirect |
| 19. C2×#638 | C2×C3 | semidirect |
| 20. C2×C4×C3⋊D3 | C2×C3 | semidirect |
| 23. #3757 | C2×C3 | semidirect |
| 24. C4⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 33. C2×C3×C3⋊D3 | D4 | semidirect |
| 34. C33×C4 | D4 | semidirect |
| 65. C2×C3×D4 | C3×D3 | semidirect |
| 66. C2×C3×D4 | C3⋊D3 | semidirect |
| 88. C2×C3⋊D3 | C3×D4 | semidirect |
| 93. C32×C4 | #67 | semidirect |
| 94. C32×C4 | C3×D4 | semidirect |
| 100. C33 | #121 | semidirect |
| 135. C2×D4 | C3×C3⋊D3 | semidirect |
| 160. C3×C4 | C3×#67 | semidirect |
| 161. C3×C4 | #638 | semidirect |
| 165. C32 | #938 | semidirect |
| 166. C32 | C3×#121 | semidirect |
| 198. C4 | C3×#638 | semidirect |
| 200. C3 | C3×#938 | semidirect |
| 201. C3 | #64147 | 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 |
| C2×C3×C4×C3⋊D3 | 2 |
| C3×#3757 | 2 |
| C3×C4⋊(C3⋊Dic3) | 2 |
| #64147 | 3 |
| C3×#938 | 3 |