Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
398 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 134 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. C3×#926 | C2 | semidirect |
| 3. C3×#834 | C2 | semidirect |
| 5. #5240 | C3 | direct (N × H) |
| 8. C2×C32×Q8 | C4 | semidirect |
| 9. C2×C32×D4 | C4 | semidirect |
| 11. C22×C32×C4 | C4 | semidirect |
| 20. #926 | C2×C3 | semidirect |
| 22. #834 | C2×C3 | semidirect |
| 44. C2×C3×Q8 | Dic3 | semidirect |
| 45. C2×C3×Q8 | C3×C4 | semidirect |
| 48. C2×C3×D4 | Dic3 | semidirect |
| 49. C2×C3×D4 | C3×C4 | semidirect |
| 54. C22×C3×C4 | Dic3 | semidirect |
| 55. C22×C3×C4 | C3×C4 | semidirect |
| 121. C2×Q8 | C3×Dic3 | semidirect |
| 122. C2×D4 | C3×Dic3 | semidirect |
| 124. C22×C4 | C3×Dic3 | semidirect |
| 158. C32 | #410 | semidirect |
| 195. C3 | #5240 | direct (N × H) |
| 196. C3 | C3×#410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#41 | 2 |
| C3×#926 | 2 |
| C3×#834 | 2 |
| C3×#410 | 3 |
| #5240 | 3 |