Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
494 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 102 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×#214 | C2 | semidirect |
| 3. C3×#924 | C2 | semidirect |
| 4. C3×#832 | C2 | semidirect |
| 5. C3×#830 | C2 | semidirect |
| 7. #5218 | C3 | direct (N × H) |
| 13. C2×C3×Dic6 | C22 | semidirect |
| 16. C3×C4⋊Dic3 | C22 | semidirect |
| 18. C2×C3×C3⋊C8 | C22 | semidirect |
| 24. C2×#214 | C2×C3 | semidirect |
| 25. #924 | C2×C3 | semidirect |
| 28. #832 | C2×C3 | semidirect |
| 29. #830 | C2×C3 | semidirect |
| 62. C2×Dic6 | C22×C3 | semidirect |
| 70. C4⋊Dic3 | C22×C3 | semidirect |
| 72. C2×C3⋊C8 | C22×C3 | semidirect |
| 79. C22×C32 | SD16 | semidirect |
| 167. C22×C3 | #214 | semidirect |
| 168. C22×C3 | C3×SD16 | semidirect |
| 181. C32 | #450 | semidirect |
| 218. C22 | C3×#214 | semidirect |
| 225. C3 | #5218 | direct (N × H) |
| 226. C3 | C3×#450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D4 | 2 |
| C2×C3×#214 | 2 |
| C3×#924 | 2 |
| C3×#832 | 2 |
| C3×#830 | 2 |
| C3×#450 | 3 |
| #5218 | 3 |