Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
672 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 672 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 |
|---|---|---|
| 2. C2×C3×#634 | C2 | semidirect |
| 3. C32×C4×Dic3 | C2 | semidirect |
| 4. #88804 | C2 | semidirect |
| 16. C2×#634 | D3 | semidirect |
| 20. C3×C4×Dic3 | D3 | semidirect |
| 56. C4×Dic3 | C3⋊D3 | semidirect |
| 74. C33 | #124 | semidirect |
| 120. C32 | #875 | semidirect |
| 121. C32 | #947 | semidirect |
| 144. C3 | #63864 | semidirect |
| 145. C3 | #64084 | 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×C3×#634 | 2 |
| C32×C4×Dic3 | 2 |
| #88804 | 2 |
| #64084 | 3 |
| #63864 | 3 |