Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
562 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 562 conjugacy classes of subgroups — too many to draw. Only its 144 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×#239 | C2 | semidirect |
| 2. C2×#3795 | C2 | semidirect |
| 3. C2×#3756 | C2 | semidirect |
| 4. C2×C3×#215 | C2 | semidirect |
| 5. #63947 | C2 | direct (N × H) |
| 6. C2×#3716 | C2 | semidirect |
| 7. C2×#3713 | C2 | semidirect |
| 8. C2×D3×C3⋊C8 | C2 | semidirect |
| 14. C3×#239 | C22 | semidirect |
| 23. #3795 | C22 | semidirect |
| 24. #3756 | C22 | semidirect |
| 26. C3×#215 | C22 | semidirect |
| 28. #3716 | C22 | semidirect |
| 29. #3713 | C22 | semidirect |
| 30. D3×C3⋊C8 | C22 | semidirect |
| 32. C2×#239 | D3 | semidirect |
| 40. C2×#215 | D3 | semidirect |
| 86. #239 | C2×D3 | semidirect |
| 105. #215 | C2×D3 | semidirect |
| 190. C2×C32 | #135 | semidirect |
| 244. C32 | C2×#135 | semidirect |
| 273. C2×C3 | #916 | semidirect |
| 274. C2×C3 | #950 | semidirect |
| 293. C3 | C2×#916 | semidirect |
| 294. C3 | C2×#950 | semidirect |
| 298. C2 | #63947 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#239 | 2 |
| C2×#3795 | 2 |
| C2×#3756 | 2 |
| C2×C3×#215 | 2 |
| #63947 | 2 |
| C2×#3716 | 2 |
| C2×#3713 | 2 |
| C2×D3×C3⋊C8 | 2 |
| C2×#950 | 3 |
| C2×#916 | 3 |