Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
486 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 152 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. C3×Q8×A4 | C2 | direct (N × H) |
| 3. C23×C3×Q8 | C3 | semidirect |
| 4. C2×Q8×A4 | C3 | direct (N × H) |
| 11. C22×C3×Q8 | C2×C3 | semidirect |
| 13. Q8×A4 | C2×C3 | direct (N × H) |
| 15. C2×C3×A4 | Q8 | direct (N × H) |
| 19. C23×Q8 | C32 | semidirect |
| 29. C2×C3×Q8 | A4 | direct (N × H) |
| 36. C3×A4 | C2×Q8 | direct (N × H) |
| 41. C22×Q8 | C2×C32 | semidirect |
| 46. C23×C3 | C3×Q8 | semidirect |
| 48. C2×A4 | C3×Q8 | direct (N × H) |
| 53. C3×Q8 | C2×A4 | direct (N × H) |
| 70. C2×Q8 | C3×A4 | direct (N × H) |
| 83. C22×C3 | C2×C3×Q8 | semidirect |
| 85. A4 | C2×C3×Q8 | direct (N × H) |
| 93. C23 | C32×Q8 | semidirect |
| 97. Q8 | C2×C3×A4 | direct (N × H) |
| 109. C2×C3 | Q8×A4 | direct (N × H) |
| 118. C22 | C2×C32×Q8 | semidirect |
| 123. C3 | C2×Q8×A4 | direct (N × H) |
| 127. C2 | C3×Q8×A4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×A4 | 2 |
| C2×C3×C4×A4 | 2 |
| C23×C3×Q8 | 3 |
| C2×Q8×A4 | 3 |
| C2×C32×Q8 | 4 |