Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
774 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 774 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. C32×H(5,𝔽2) | C2 | semidirect |
| 2. #64367 | C2 | semidirect |
| 3. #64160 | C2 | semidirect |
| 4. #64159 | C2 | semidirect |
| 5. #64157 | C2 | semidirect |
| 6. C2×#3754 | C2 | semidirect |
| 7. #64141 | C2 | semidirect |
| 16. #3828 | C22 | semidirect |
| 17. C2×#634 | C22 | semidirect |
| 18. #3756 | C22 | semidirect |
| 19. #3755 | C22 | semidirect |
| 20. #3754 | C22 | semidirect |
| 21. #3754 | C22 | semidirect |
| 22. #3753 | C22 | semidirect |
| 23. #3748 | C22 | semidirect |
| 24. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 25. C3×H(5,𝔽2) | D3 | semidirect |
| 75. H(5,𝔽2) | C3⋊D3 | semidirect |
| 126. C32 | #577 | semidirect |
| 156. C3 | #5836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×H(5,𝔽2) | 2 |
| #64367 | 2 |
| #64160 | 2 |
| #64159 | 2 |
| #64157 | 2 |
| C2×#3754 | 2 |
| #64141 | 2 |
| #5836 | 3 |