Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
406 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 94 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. C2×C32×#41 | C2 | semidirect |
| 2. C2×C3×#215 | C2 | semidirect |
| 3. C2×C3×#213 | C2 | semidirect |
| 4. C3×#930 | C2 | semidirect |
| 5. C3×#835 | C2 | semidirect |
| 6. C3×#832 | C2 | semidirect |
| 7. C3×#830 | C2 | semidirect |
| 9. #5238 | C3 | direct (N × H) |
| 26. C2×C3×#41 | D3 | semidirect |
| 27. C2×C3×#41 | C2×C3 | semidirect |
| 31. C2×#215 | C2×C3 | semidirect |
| 32. C2×#213 | C2×C3 | semidirect |
| 33. #930 | C2×C3 | semidirect |
| 37. #835 | C2×C3 | semidirect |
| 38. #832 | C2×C3 | semidirect |
| 39. #830 | C2×C3 | semidirect |
| 44. C32×Q8 | D4 | semidirect |
| 47. C32×D4 | D4 | semidirect |
| 113. C2×#41 | C3×D3 | semidirect |
| 132. C3×Q8 | #67 | semidirect |
| 133. C3×Q8 | C3×D4 | semidirect |
| 144. C3×D4 | #67 | semidirect |
| 145. C3×D4 | C3×D4 | semidirect |
| 235. C32 | #449 | semidirect |
| 240. Q8 | C3×#67 | semidirect |
| 246. D4 | C3×#67 | semidirect |
| 289. C3 | #5238 | direct (N × H) |
| 290. C3 | C3×#449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#41 | 2 |
| C2×C3×#215 | 2 |
| C2×C3×#213 | 2 |
| C3×#930 | 2 |
| C3×#835 | 2 |
| C3×#832 | 2 |
| C3×#830 | 2 |
| C3×#449 | 3 |
| #5238 | 3 |