Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
774 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 191 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×Q8×C3⋊D3 | C2 | semidirect |
| 3. C2×C32×Q16 | C2 | semidirect |
| 4. C2×#3756 | C2 | semidirect |
| 5. C2×#3755 | C2 | semidirect |
| 6. #64127 | C2 | direct (N × H) |
| 7. C2×#3744 | C2 | semidirect |
| 8. C2×#3743 | C2 | semidirect |
| 15. Q8×C3⋊D3 | C22 | semidirect |
| 23. C32×Q16 | C22 | semidirect |
| 25. #3756 | C22 | semidirect |
| 26. #3755 | C22 | semidirect |
| 28. #3744 | C22 | semidirect |
| 29. #3743 | C22 | semidirect |
| 32. C2×C3×Q16 | D3 | semidirect |
| 75. C3×Q16 | C2×D3 | semidirect |
| 97. C2×Q16 | C3⋊D3 | semidirect |
| 124. C2×C32 | #137 | semidirect |
| 142. Q16 | C2×C3⋊D3 | semidirect |
| 159. C32 | C2×#137 | semidirect |
| 183. C2×C3 | #918 | semidirect |
| 198. C3 | C2×#918 | semidirect |
| 201. C2 | #64127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3832 | 2 |
| C2×Q8×C3⋊D3 | 2 |
| C2×C32×Q16 | 2 |
| C2×#3756 | 2 |
| C2×#3755 | 2 |
| #64127 | 2 |
| C2×#3744 | 2 |
| C2×#3743 | 2 |
| C2×#918 | 3 |