Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
666 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 205 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. C32×C4×Q8 | C2 | semidirect |
| 3. #64153 | C2 | semidirect |
| 6. #64098 | C2 | semidirect |
| 7. #64097 | C2 | semidirect |
| 10. C4×#634 | C2 | semidirect |
| 11. C4×#634 | C2 | semidirect |
| 36. C3×C4×Q8 | D3 | semidirect |
| 61. C4×C3⋊D3 | Q8 | semidirect |
| 110. C4×Q8 | C3⋊D3 | semidirect |
| 171. C32 | #533 | semidirect |
| 207. C3 | #5578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q8 | 2 |
| #64155 | 2 |
| #64153 | 2 |
| #64106 | 2 |
| #64105 | 2 |
| #64098 | 2 |
| #64097 | 2 |
| #64081 | 2 |
| C42×C3⋊D3 | 2 |
| C4×#634 | 2 |
| #5578 | 3 |