Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
558 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 101 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. M16×C3⋊D3 | C2 | semidirect |
| 3. C32×#100 | C2 | semidirect |
| 4. #63660 | C2 | semidirect |
| 5. #63650 | C2 | semidirect |
| 14. C32×M16 | C22 | semidirect |
| 15. #3748 | C22 | semidirect |
| 20. C3×#100 | D3 | semidirect |
| 46. C3×M16 | C2×D3 | semidirect |
| 66. #100 | C3⋊D3 | direct (N × H) |
| 87. C3⋊D3 | #100 | direct (N × H) |
| 97. M16 | C2×C3⋊D3 | semidirect |
| 111. C32 | C2×#100 | semidirect |
| 145. C3 | D3×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×C3⋊D3 | 2 |
| M16×C3⋊D3 | 2 |
| C32×#100 | 2 |
| #63660 | 2 |
| #63650 | 2 |
| D3×#100 | 3 |