Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 99 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×#3744 | C2 | semidirect |
| 2. C2×C8×C3⋊D3 | C2 | semidirect |
| 3. #64106 | C2 | semidirect |
| 5. C32×#106 | C2 | semidirect |
| 6. #63637 | C2 | semidirect |
| 7. #63636 | C2 | semidirect |
| 26. C3×#106 | D3 | semidirect |
| 43. C32×C8 | D4 | semidirect |
| 65. C2×C3⋊D3 | SD16 | semidirect |
| 76. #106 | C3⋊D3 | semidirect |
| 93. C3×C8 | D12 | semidirect |
| 126. C32 | #465 | semidirect |
| 142. C8 | C4⋊(C3⋊D3) | semidirect |
| 161. C3 | #4864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3744 | 2 |
| C2×C8×C3⋊D3 | 2 |
| #64106 | 2 |
| #64104 | 2 |
| C32×#106 | 2 |
| #63637 | 2 |
| #63636 | 2 |
| #4864 | 3 |