Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
786 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 219 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×#3828 | C2 | semidirect |
| 3. #64160 | C2 | semidirect |
| 4. #64159 | C2 | semidirect |
| 5. #64158 | C2 | semidirect |
| 6. #64151 | C2 | semidirect |
| 7. #64141 | C2 | semidirect |
| 8. C2×#3748 | C2 | semidirect |
| 13. C32×#41 | C22 | semidirect |
| 14. C2×C32×Q8 | C22 | semidirect |
| 16. C2×C32×D4 | C22 | semidirect |
| 23. #3828 | C22 | semidirect |
| 24. C2×C4⋊(C3⋊D3) | C22 | semidirect |
| 26. C2×#634 | C22 | semidirect |
| 27. #3756 | C22 | semidirect |
| 28. #3755 | C22 | semidirect |
| 29. #3754 | C22 | semidirect |
| 30. #3753 | C22 | semidirect |
| 31. #3748 | C22 | semidirect |
| 32. #3748 | C22 | semidirect |
| 33. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 34. C2×C3×#41 | D3 | semidirect |
| 74. C3×#41 | C2×D3 | semidirect |
| 75. C2×C3×Q8 | C2×D3 | semidirect |
| 77. C2×C3×D4 | C2×D3 | semidirect |
| 110. C2×#41 | C3⋊D3 | semidirect |
| 158. #41 | C2×C3⋊D3 | semidirect |
| 160. C2×Q8 | C2×C3⋊D3 | semidirect |
| 164. C2×D4 | C2×C3⋊D3 | semidirect |
| 189. C32 | #575 | semidirect |
| 238. C3 | #5822 | 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×#3828 | 2 |
| #64160 | 2 |
| #64159 | 2 |
| #64158 | 2 |
| #64151 | 2 |
| #64141 | 2 |
| C2×#3748 | 2 |
| #5822 | 3 |