Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
312 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 93 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. #64116 | C2 | semidirect |
| 3. C32×#108 | C2 | semidirect |
| 4. #63652 | C2 | semidirect |
| 5. #63642 | C2 | semidirect |
| 12. #3746 | C4 | semidirect |
| 13. #3745 | C4 | semidirect |
| 14. #3744 | C4 | semidirect |
| 19. C3×#108 | D3 | semidirect |
| 51. #108 | C3⋊D3 | semidirect |
| 83. C32 | #444 | semidirect |
| 103. C3 | #4894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #64116 | 2 |
| #64113 | 2 |
| C32×#108 | 2 |
| #63652 | 2 |
| #63642 | 2 |
| #4894 | 3 |