Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
350 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 76 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×C3×D3×Q8 | C2 | semidirect |
| 2. C2×#3755 | C2 | semidirect |
| 4. C2×#3717 | C2 | semidirect |
| 5. C3×#835 | C2 | semidirect |
| 6. #63565 | C2 | semidirect |
| 7. (C2×D3)⋊(C3⋊C8) | C2 | semidirect |
| 26. C2×D3×Q8 | D3 | semidirect |
| 36. #835 | D3 | semidirect |
| 43. C32×Q8 | D4 | semidirect |
| 56. C3×Dic6 | D4 | semidirect |
| 101. C2×C3×D3 | SD16 | semidirect |
| 127. C3×Q8 | D12 | semidirect |
| 128. C3×Q8 | #67 | semidirect |
| 157. Dic6 | #67 | semidirect |
| 200. C2×D3 | #215 | semidirect |
| 216. C32 | #448 | semidirect |
| 223. Q8 | #626 | semidirect |
| 265. C3 | #4806 | semidirect |
| 266. C3 | #5227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×Q8 | 2 |
| C2×#3755 | 2 |
| #63909 | 2 |
| C2×#3717 | 2 |
| C3×#835 | 2 |
| #63565 | 2 |
| (C2×D3)⋊(C3⋊C8) | 2 |
| #5227 | 3 |
| #4806 | 3 |