Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
684 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 128 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. C2×Dic3×C3⋊D3 | C2 | semidirect |
| 3. C2×D3×C3⋊Dic3 | C2 | semidirect |
| 4. C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 5. C3×#3752 | C2 | semidirect |
| 6. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 7. #88806 | C2 | semidirect |
| 17. #6290 | C4 | semidirect |
| 27. #3752 | D3 | semidirect |
| 33. C3×(C2×D3)⋊C4 | D3 | semidirect |
| 38. C2×C3×C3⋊D3 | C2×C4 | semidirect |
| 41. C2×C32×D3 | C2×C4 | semidirect |
| 43. C3⋊(C3⋊Dic3) | C2×C4 | semidirect |
| 44. C3⋊(C3⋊Dic3) | D4 | semidirect |
| 86. (C2×D3)⋊C4 | C3⋊D3 | semidirect |
| 100. C2×C3⋊D3 | C4×D3 | semidirect |
| 106. C2×C3×D3 | C4×D3 | semidirect |
| 121. C33 | C4×D4 | semidirect |
| 179. C2×D3 | C4×C3⋊D3 | semidirect |
| 194. C32 | #67⋊C4 | semidirect |
| 195. C32 | #67⋊C4 | semidirect |
| 232. C3 | #63902 | semidirect |
| 233. C3 | #64090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6290 | 2 |
| C2×Dic3×C3⋊D3 | 2 |
| C2×D3×C3⋊Dic3 | 2 |
| C4×C3⋊(C3⋊Dic3) | 2 |
| C3×#3752 | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| #88806 | 2 |
| #64090 | 3 |
| #63902 | 3 |