Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
194 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 70 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×C32×Q16 | C2 | semidirect |
| 3. C3×#829 | C2 | semidirect |
| 4. C3×#828 | C2 | semidirect |
| 5. C3×#812 | C2 | semidirect |
| 7. #5179 | C3 | direct (N × H) |
| 19. C2×C3×Q16 | D3 | semidirect |
| 20. C2×C3×Q16 | C2×C3 | semidirect |
| 25. #829 | C2×C3 | semidirect |
| 26. #828 | C2×C3 | semidirect |
| 27. #812 | C2×C3 | semidirect |
| 68. C2×Q16 | C3×D3 | semidirect |
| 126. C32 | #510 | semidirect |
| 152. C3 | #5179 | direct (N × H) |
| 153. C3 | C3×#510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q16 | 2 |
| C3×#904 | 2 |
| C3×#829 | 2 |
| C3×#828 | 2 |
| C3×#812 | 2 |
| C3×#510 | 3 |
| #5179 | 3 |