Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
440 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 440 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. C2×C32×Dic6 | C2 | semidirect |
| 3. #88855 | C2 | semidirect |
| 4. #88798 | C2 | semidirect |
| 5. #88793 | C2 | semidirect |
| 20. C2×C3×Dic6 | D3 | semidirect |
| 62. C2×Dic6 | C3⋊D3 | semidirect |
| 86. C33 | #137 | semidirect |
| 136. C32 | #942 | semidirect |
| 137. C32 | #951 | semidirect |
| 162. C3 | #63827 | semidirect |
| 163. C3 | #64151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3828 | 2 |
| C2×C32×Dic6 | 2 |
| #88855 | 2 |
| #88798 | 2 |
| #88793 | 2 |
| #64151 | 3 |
| #63827 | 3 |