Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
512 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 512 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 |
|---|---|---|
| 1. C2×#6308 | C2 | semidirect |
| 3. C32×#208 | C2 | semidirect |
| 4. #88800 | C2 | semidirect |
| 5. #88796 | C2 | semidirect |
| 25. C3×#208 | D3 | semidirect |
| 69. #208 | C3⋊D3 | semidirect |
| 89. C33 | #137 | semidirect |
| 142. C32 | #909 | semidirect |
| 143. C32 | #951 | semidirect |
| 168. C3 | #63831 | semidirect |
| 169. C3 | #64118 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6308 | 2 |
| C3×#3828 | 2 |
| C32×#208 | 2 |
| #88800 | 2 |
| #88796 | 2 |
| #64118 | 3 |
| #63831 | 3 |