Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
246 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 83 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. #63656 | C2 | semidirect |
| 4. #63655 | C2 | semidirect |
| 5. #63639 | C2 | semidirect |
| 16. C2×C3×Q16 | D3 | semidirect |
| 48. C2×Q16 | C3⋊D3 | semidirect |
| 80. C32 | #510 | semidirect |
| 100. C3 | #5179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q16 | 2 |
| #64113 | 2 |
| #63656 | 2 |
| #63655 | 2 |
| #63639 | 2 |
| #5179 | 3 |