Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
840 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 251 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×Q8×C3⋊D3 | C2 | semidirect |
| 2. C32×C4×Q8 | C2 | semidirect |
| 3. #64106 | C2 | semidirect |
| 5. #64078 | C2 | semidirect |
| 18. C3×C4×Q8 | D3 | semidirect |
| 23. C32×Q8 | D4 | semidirect |
| 28. C4⋊(C3⋊D3) | Q8 | direct (N × H) |
| 45. C2×C3⋊D3 | C2×Q8 | semidirect |
| 48. C32×C4 | C2×Q8 | semidirect |
| 53. C4×Q8 | C3⋊D3 | semidirect |
| 56. C3×Q8 | D12 | semidirect |
| 84. C3×C4 | D3×Q8 | semidirect |
| 86. C32 | D4×Q8 | semidirect |
| 89. Q8 | C4⋊(C3⋊D3) | direct (N × H) |
| 107. C4 | Q8×C3⋊D3 | semidirect |
| 108. C3 | Q8×D12 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊D3 | 2 |
| C32×C4×Q8 | 2 |
| #64106 | 2 |
| C4×C4⋊(C3⋊D3) | 2 |
| #64078 | 2 |
| Q8×D12 | 3 |