Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
350 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 78 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×#3710 | C2 | semidirect |
| 4. C3×(C2×D3)⋊C8 | C2 | semidirect |
| 5. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 26. (C2×D3)⋊C8 | D3 | semidirect |
| 142. C32 | #408 | semidirect |
| 178. C3 | #4727 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3798 | 2 |
| C2×#3743 | 2 |
| C2×#3710 | 2 |
| C3×(C2×D3)⋊C8 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #4727 | 3 |