Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
394 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 102 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. C22×C32×Q8 | C2 | semidirect |
| 2. C2×C3×#215 | C2 | semidirect |
| 4. C3×#835 | C2 | semidirect |
| 5. C3×#830 | C2 | semidirect |
| 7. #5227 | C3 | direct (N × H) |
| 20. C22×C3×Q8 | D3 | semidirect |
| 21. C22×C3×Q8 | C2×C3 | semidirect |
| 24. C2×#215 | C2×C3 | semidirect |
| 28. #835 | C2×C3 | semidirect |
| 29. #830 | C2×C3 | semidirect |
| 34. C32×Q8 | D4 | semidirect |
| 74. C22×C32 | SD16 | semidirect |
| 83. C22×Q8 | C3×D3 | semidirect |
| 100. C3×Q8 | #67 | semidirect |
| 101. C3×Q8 | C3×D4 | semidirect |
| 152. C22×C3 | #215 | semidirect |
| 153. C22×C3 | C3×SD16 | semidirect |
| 170. C32 | #448 | semidirect |
| 175. Q8 | C3×#67 | semidirect |
| 204. C22 | C3×#215 | semidirect |
| 211. C3 | #5227 | direct (N × H) |
| 212. C3 | C3×#448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×Q8 | 2 |
| C2×C3×#215 | 2 |
| C3×#930 | 2 |
| C3×#835 | 2 |
| C3×#830 | 2 |
| C3×#448 | 3 |
| #5227 | 3 |