Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
336 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 97 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. Q8×C3⋊Dic3 | C2 | semidirect |
| 5. #63662 | C2 | semidirect |
| 7. #63641 | C2 | semidirect |
| 22. C2×C3×Q16 | D3 | semidirect |
| 69. C2×Q16 | C3⋊D3 | semidirect |
| 119. C32 | #464 | semidirect |
| 150. C3 | #5185 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q16 | 2 |
| #64156 | 2 |
| Q8×C3⋊Dic3 | 2 |
| C2×#3755 | 2 |
| #63662 | 2 |
| #63648 | 2 |
| #63641 | 2 |
| #5185 | 3 |