Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
774 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 259 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×C32×M16 | C2 | semidirect |
| 3. C2×#3748 | C2 | semidirect |
| 4. #64116 | C2 | semidirect |
| 5. M16×C3⋊D3 | C2 | semidirect |
| 6. #64110 | C2 | semidirect |
| 18. C32×M16 | C22 | semidirect |
| 19. C2×C32×C8 | C22 | semidirect |
| 21. #3748 | C22 | semidirect |
| 22. C2×C3⋊(C3⋊C8) | C22 | semidirect |
| 23. #3743 | C22 | semidirect |
| 24. C8×C3⋊D3 | C22 | semidirect |
| 26. C2×C3×M16 | D3 | semidirect |
| 61. C3×M16 | C2×D3 | semidirect |
| 62. C2×C3×C8 | C2×D3 | semidirect |
| 84. C2×M16 | C3⋊D3 | semidirect |
| 122. M16 | C2×C3⋊D3 | semidirect |
| 125. C2×C8 | C2×C3⋊D3 | semidirect |
| 137. C32 | #568 | semidirect |
| 173. C3 | #5745 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3828 | 2 |
| C2×C32×M16 | 2 |
| C2×#3748 | 2 |
| #64116 | 2 |
| M16×C3⋊D3 | 2 |
| #64110 | 2 |
| #5745 | 3 |