Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
193 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 193 conjugacy classes of subgroups — too many to draw. Only its 62 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 |
|---|---|---|
| 1. C3×#919 | C2 | semidirect |
| 2. C3×D3×D8 | C2 | semidirect |
| 3. C32×SD32 | C2 | semidirect |
| 4. C3×#828 | C2 | semidirect |
| 5. C3×#826 | C2 | semidirect |
| 6. C3×D48 | C2 | semidirect |
| 7. C3×#798 | C2 | semidirect |
| 9. #4914 | C3 | direct (N × H) |
| 12. C32×Q16 | C22 | semidirect |
| 17. C3×D24 | C22 | semidirect |
| 19. C32×C16 | C22 | semidirect |
| 20. C3×C3⋊C16 | C22 | semidirect |
| 23. #919 | C2×C3 | semidirect |
| 24. D3×D8 | C2×C3 | semidirect |
| 27. C3×SD32 | D3 | semidirect |
| 28. C3×SD32 | C2×C3 | semidirect |
| 32. #828 | C2×C3 | semidirect |
| 33. #826 | C2×C3 | semidirect |
| 34. D48 | C2×C3 | semidirect |
| 35. #798 | C2×C3 | semidirect |
| 53. C3×Q16 | C2×D3 | semidirect |
| 54. C3×Q16 | C22×C3 | semidirect |
| 66. D24 | C22×C3 | semidirect |
| 70. C3×C16 | C2×D3 | semidirect |
| 71. C3×C16 | C22×C3 | semidirect |
| 72. C3⋊C16 | C22×C3 | semidirect |
| 84. SD32 | C3×D3 | semidirect |
| 120. Q16 | C2×C3×D3 | semidirect |
| 128. C16 | C2×C3×D3 | semidirect |
| 148. C32 | #509 | semidirect |
| 181. C3 | #4914 | direct (N × H) |
| 182. C3 | C3×#509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#919 | 2 |
| C3×D3×D8 | 2 |
| C32×SD32 | 2 |
| C3×#828 | 2 |
| C3×#826 | 2 |
| C3×D48 | 2 |
| C3×#798 | 2 |
| C3×#509 | 3 |
| #4914 | 3 |