Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
780 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 780 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 |
|---|---|---|
| 1. C2×C4×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. C2×Dic3×C3⋊D3 | C2 | semidirect |
| 4. C3×#3752 | C2 | semidirect |
| 5. C32×Dic3⋊C4 | C2 | semidirect |
| 6. #88804 | C2 | semidirect |
| 7. Dic3×C3⋊Dic3 | C2 | semidirect |
| 18. #6292 | C4 | semidirect |
| 29. #3752 | D3 | semidirect |
| 32. C3×Dic3⋊C4 | D3 | semidirect |
| 38. C2×C3⋊(C3⋊D3) | C2×C4 | semidirect |
| 41. C2×C3×C3⋊D3 | C2×C4 | semidirect |
| 43. C3⋊(C3⋊Dic3) | D4 | semidirect |
| 46. C32×Dic3 | C2×C4 | semidirect |
| 90. Dic3⋊C4 | C3⋊D3 | semidirect |
| 107. C2×C3⋊D3 | C4×D3 | semidirect |
| 122. C3×Dic3 | C4×D3 | semidirect |
| 124. C33 | C4×D4 | semidirect |
| 199. Dic3 | C4×C3⋊D3 | semidirect |
| 201. C32 | #67⋊C4 | semidirect |
| 202. C32 | #893 | semidirect |
| 240. C3 | #63881 | semidirect |
| 241. C3 | #64102 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C3⋊(C3⋊D3) | 2 |
| C2×#6292 | 2 |
| C2×Dic3×C3⋊D3 | 2 |
| C3×#3752 | 2 |
| C32×Dic3⋊C4 | 2 |
| #88804 | 2 |
| Dic3×C3⋊Dic3 | 2 |
| #64102 | 3 |
| #63881 | 3 |