Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
474 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×C32×SD16 | C2 | semidirect |
| 4. C2×#3754 | C2 | semidirect |
| 5. #63662 | C2 | semidirect |
| 6. #63647 | C2 | semidirect |
| 7. #63643 | C2 | semidirect |
| 25. C2×C3×SD16 | D3 | semidirect |
| 34. C32×Q8 | D4 | semidirect |
| 48. #634 | D4 | semidirect |
| 73. C2×C3⋊D3 | SD16 | semidirect |
| 82. C2×SD16 | C3⋊D3 | semidirect |
| 90. C3×Q8 | #67 | semidirect |
| 140. C32 | #448 | semidirect |
| 147. Q8 | #638 | semidirect |
| 179. C3 | #5170 | 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 |
| C2×C32×SD16 | 2 |
| #64147 | 2 |
| C2×#3754 | 2 |
| #63662 | 2 |
| #63647 | 2 |
| #63643 | 2 |
| #5170 | 3 |