Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
270 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 4. #63576 | C2 | semidirect |
| 5. #63574 | C2 | semidirect |
| 10. #3748 | C4 | semidirect |
| 38. C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 145. C32 | #428 | semidirect |
| 179. C3 | #4964 | semidirect |
| 180. C3 | #4995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3748 | 2 |
| C3×#926 | 2 |
| C2×C3×C4⋊Dic3 | 2 |
| #63576 | 2 |
| #63574 | 2 |
| #4995 | 3 |
| #4964 | 3 |