Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
780 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 254 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. C22×C3×C3⋊Dic3 | C2 | semidirect |
| 3. C3×#3757 | C2 | semidirect |
| 4. C3×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 5. C3×C4×C3⋊Dic3 | C2 | semidirect |
| 6. D4×C3⋊Dic3 | C3 | direct (N × H) |
| 9. C33×D4 | C4 | semidirect |
| 18. C22×C3⋊Dic3 | C2×C3 | semidirect |
| 20. #3757 | C2×C3 | semidirect |
| 21. C4⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 22. C4×C3⋊Dic3 | C2×C3 | semidirect |
| 28. C22×C33 | C2×C4 | semidirect |
| 30. C33×C4 | C2×C4 | semidirect |
| 33. C3×C3⋊Dic3 | D4 | direct (N × H) |
| 40. C32×D4 | Dic3 | semidirect |
| 41. C32×D4 | C3×C4 | semidirect |
| 76. C22×C32 | C2×Dic3 | semidirect |
| 77. C22×C32 | C2×C3×C4 | semidirect |
| 81. C32×C4 | C2×Dic3 | semidirect |
| 82. C32×C4 | C2×C3×C4 | semidirect |
| 85. C3⋊Dic3 | C3×D4 | direct (N × H) |
| 90. C33 | C4×D4 | semidirect |
| 95. C3×D4 | C3×Dic3 | semidirect |
| 96. C3×D4 | C3⋊Dic3 | direct (N × H) |
| 133. C22×C3 | C2×C3×Dic3 | semidirect |
| 134. C22×C3 | C2×C3⋊Dic3 | semidirect |
| 141. C3×C4 | C2×C3×Dic3 | semidirect |
| 142. C3×C4 | C2×C3⋊Dic3 | semidirect |
| 147. C32 | D4×Dic3 | semidirect |
| 148. C32 | C3×C4×D4 | semidirect |
| 150. D4 | C3×C3⋊Dic3 | direct (N × H) |
| 170. C22 | C2×C3×C3⋊Dic3 | semidirect |
| 175. C4 | C2×C3×C3⋊Dic3 | semidirect |
| 177. C3 | C3×D4×Dic3 | semidirect |
| 178. C3 | D4×C3⋊Dic3 | 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 |
| C22×C3×C3⋊Dic3 | 2 |
| C3×#3757 | 2 |
| C3×C4⋊(C3⋊Dic3) | 2 |
| C3×C4×C3⋊Dic3 | 2 |
| D4×C3⋊Dic3 | 3 |
| C3×D4×Dic3 | 3 |