Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
406 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 72 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. #63818 | C2 | semidirect |
| 4. C3×#823 | C2 | semidirect |
| 5. #63558 | C2 | semidirect |
| 15. C32×M16 | C22 | semidirect |
| 16. #3748 | C22 | semidirect |
| 19. C3×#208 | C22 | semidirect |
| 29. #823 | D3 | semidirect |
| 61. C3×M16 | C2×D3 | semidirect |
| 64. #208 | C2×D3 | semidirect |
| 122. C3⋊D3 | #100 | semidirect |
| 136. M16 | D32 | semidirect |
| 161. C32 | C2×#100 | semidirect |
| 203. C3 | D3×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3802 | 2 |
| M16×C3⋊D3 | 2 |
| #63818 | 2 |
| C3×#823 | 2 |
| #63558 | 2 |
| D3×#100 | 3 |