Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
291 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 94 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. C32×C4×Q8 | C2 | semidirect |
| 2. C2×C3×#215 | C2 | semidirect |
| 4. C3×#809 | C2 | semidirect |
| 5. C3×C4⋊(C3⋊C8) | C2 | semidirect |
| 7. #5027 | C3 | direct (N × H) |
| 21. C3×C4×Q8 | D3 | semidirect |
| 22. C3×C4×Q8 | C2×C3 | semidirect |
| 23. C2×#215 | C2×C3 | semidirect |
| 27. #809 | C2×C3 | semidirect |
| 28. C4⋊(C3⋊C8) | C2×C3 | semidirect |
| 31. C32×Q8 | D4 | semidirect |
| 75. C32×C4 | SD16 | semidirect |
| 80. C4×Q8 | C3×D3 | semidirect |
| 89. C3×Q8 | D12 | semidirect |
| 90. C3×Q8 | C3×D4 | semidirect |
| 151. C3×C4 | #215 | semidirect |
| 152. C3×C4 | C3×SD16 | semidirect |
| 157. C32 | #460 | semidirect |
| 160. Q8 | C3×D12 | semidirect |
| 189. C4 | C3×#215 | semidirect |
| 193. C3 | #5027 | direct (N × H) |
| 194. C3 | C3×#460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q8 | 2 |
| C2×C3×#215 | 2 |
| C3×#874 | 2 |
| C3×#809 | 2 |
| C3×C4⋊(C3⋊C8) | 2 |
| C3×#460 | 3 |
| #5027 | 3 |