Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
401 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 401 conjugacy classes of subgroups — too many to draw. Only its 68 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×C3×#204 | C2 | semidirect |
| 3. #63871 | C2 | semidirect |
| 4. C2×#3715 | C2 | semidirect |
| 5. #63647 | C2 | semidirect |
| 6. C3×#821 | C2 | semidirect |
| 7. #63562 | C2 | semidirect |
| 14. C2×C3×Dic6 | C22 | semidirect |
| 18. C2×C32×C8 | C22 | semidirect |
| 19. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 20. C3×C4⋊Dic3 | C22 | semidirect |
| 31. C2×#204 | D3 | semidirect |
| 35. #821 | D3 | semidirect |
| 78. C2×Dic6 | C2×D3 | semidirect |
| 81. C2×C3×C8 | C2×D3 | semidirect |
| 82. C2×C3×C8 | C2×D3 | semidirect |
| 89. C4⋊Dic3 | C2×D3 | semidirect |
| 98. C2×C3⋊D3 | SD16 | semidirect |
| 184. C2×C8 | D32 | semidirect |
| 227. C32 | #450 | semidirect |
| 282. C3 | #4776 | semidirect |
| 283. C3 | #5169 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3802 | 2 |
| C2×C3×#204 | 2 |
| #63871 | 2 |
| C2×#3715 | 2 |
| #63647 | 2 |
| C3×#821 | 2 |
| #63562 | 2 |
| #5169 | 3 |
| #4776 | 3 |