Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
580 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 580 conjugacy classes of subgroups — too many to draw. Only its 110 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×#6293 | C2 | semidirect |
| 4. C3×#3750 | C2 | semidirect |
| 5. C32×C4⋊Dic3 | C2 | semidirect |
| 6. #88807 | C2 | semidirect |
| 29. #3750 | D3 | semidirect |
| 30. C3×C4⋊Dic3 | D3 | semidirect |
| 37. C2×C3⋊(C3⋊D3) | Q8 | semidirect |
| 83. C4⋊Dic3 | C3⋊D3 | semidirect |
| 113. C33 | C22⋊Q8 | semidirect |
| 181. C32 | #896 | semidirect |
| 182. C32 | #897 | semidirect |
| 215. C3 | #63895 | semidirect |
| 216. C3 | #64105 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6293 | 2 |
| C2×#6289 | 2 |
| #88859 | 2 |
| C3×#3750 | 2 |
| C32×C4⋊Dic3 | 2 |
| #88807 | 2 |
| #88804 | 2 |
| #64105 | 3 |
| #63895 | 3 |