Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
496 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 104 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. C3×#3750 | C2 | semidirect |
| 3. C32×C4×Dic3 | C2 | semidirect |
| 4. #88807 | C2 | semidirect |
| 5. #88806 | C2 | semidirect |
| 25. #3750 | D3 | semidirect |
| 27. C3×C4×Dic3 | D3 | semidirect |
| 79. C4×Dic3 | C3⋊D3 | semidirect |
| 107. C33 | #126 | semidirect |
| 171. C32 | #876 | semidirect |
| 172. C32 | #898 | semidirect |
| 203. C3 | #63868 | semidirect |
| 204. C3 | #64085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88859 | 2 |
| C3×#3750 | 2 |
| C32×C4×Dic3 | 2 |
| #88807 | 2 |
| #88806 | 2 |
| #88804 | 2 |
| #64085 | 3 |
| #63868 | 3 |