Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
278 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 86 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×#944 | C2 | semidirect |
| 4. C2×C3×#216 | C2 | semidirect |
| 7. C3×#815 | C2 | semidirect |
| 9. #5190 | C3 | direct (N × H) |
| 25. C2×C3×Q16 | D3 | semidirect |
| 26. C2×C3×Q16 | C2×C3 | semidirect |
| 32. #944 | C2×C3 | semidirect |
| 33. C2×#216 | C2×C3 | semidirect |
| 37. #815 | C2×C3 | semidirect |
| 95. C2×Q16 | C3×D3 | semidirect |
| 180. C32 | #497 | semidirect |
| 215. C3 | #5190 | direct (N × H) |
| 216. C3 | C3×#497 | 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×#947 | 2 |
| C3×#944 | 2 |
| C2×C3×#216 | 2 |
| C2×C3×#215 | 2 |
| C2×C3×#204 | 2 |
| C3×#815 | 2 |
| C3×#497 | 3 |
| #5190 | 3 |