Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
576 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 576 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×C32×Dic6 | C2 | semidirect |
| 3. C4×C3⋊(C3⋊Dic3) | C2 | semidirect |
| 4. #88803 | C2 | semidirect |
| 16. C2×C3×Dic6 | D3 | semidirect |
| 50. C2×Dic6 | C3⋊D3 | semidirect |
| 72. C33 | #124 | semidirect |
| 115. C32 | #936 | semidirect |
| 116. C32 | #947 | semidirect |
| 138. C3 | #63863 | semidirect |
| 139. C3 | #64156 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4⋊(C3⋊D3) | 2 |
| C2×C32×Dic6 | 2 |
| C4×C3⋊(C3⋊Dic3) | 2 |
| #88803 | 2 |
| #64156 | 3 |
| #63863 | 3 |