Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
474 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 111 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×#3743 | C2 | semidirect |
| 3. C2×C8×C3⋊D3 | C2 | semidirect |
| 4. C32×C22⋊C8 | C2 | semidirect |
| 5. #63657 | C2 | semidirect |
| 6. #63647 | C2 | semidirect |
| 7. #63647 | C2 | semidirect |
| 27. C3×C22⋊C8 | D3 | semidirect |
| 89. C22⋊C8 | C3⋊D3 | semidirect |
| 147. C32 | #408 | semidirect |
| 190. C3 | #4727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| C2×#3743 | 2 |
| C2×C8×C3⋊D3 | 2 |
| C32×C22⋊C8 | 2 |
| #63657 | 2 |
| #63647 | 2 |
| #4727 | 3 |