Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
279 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 110 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 |
| 4. C3×#835 | C2 | semidirect |
| 6. C3×#808 | C2 | semidirect |
| 7. C3×C4×C3⋊C8 | C2 | semidirect |
| 9. C4×#215 | C3 | direct (N × H) |
| 17. C3×#215 | C4 | direct (N × H) |
| 24. C3×C4×Q8 | D3 | semidirect |
| 25. C3×C4×Q8 | C2×C3 | semidirect |
| 33. #835 | C2×C3 | semidirect |
| 35. #808 | C2×C3 | semidirect |
| 36. C4×C3⋊C8 | C2×C3 | semidirect |
| 39. C32×Q8 | C2×C4 | semidirect |
| 50. C3×C3⋊C8 | C2×C4 | semidirect |
| 76. #215 | C3×C4 | direct (N × H) |
| 88. C32×C4 | SD16 | semidirect |
| 93. C4×Q8 | C3×D3 | semidirect |
| 105. C3×Q8 | C4×D3 | semidirect |
| 106. C3×Q8 | C2×C3×C4 | semidirect |
| 133. C3⋊C8 | C2×C3×C4 | semidirect |
| 172. C3×C4 | #215 | direct (N × H) |
| 173. C3×C4 | C3×SD16 | semidirect |
| 179. C32 | C4×SD16 | semidirect |
| 182. Q8 | C3×C4×D3 | semidirect |
| 213. C4 | C3×#215 | direct (N × H) |
| 217. C3 | C4×#215 | direct (N × H) |
| 218. C3 | C3×C4×SD16 | 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×C4×D12 | 2 |
| C3×#835 | 2 |
| C3×#809 | 2 |
| C3×#808 | 2 |
| C3×C4×C3⋊C8 | 2 |
| C3×C4×SD16 | 3 |
| C4×#215 | 3 |