Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
246 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 7. #5184 | C3 | direct (N × H) |
| 9. C32×Q16 | C4 | semidirect |
| 40. C3×Q16 | Dic3 | semidirect |
| 41. C3×Q16 | C3×C4 | semidirect |
| 90. Q16 | C3×Dic3 | semidirect |
| 113. C32 | #441 | semidirect |
| 135. C3 | #5184 | direct (N × H) |
| 136. C3 | C3×#441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q16 | 2 |
| C3×Q8×Dic3 | 2 |
| C3×#835 | 2 |
| C3×#817 | 2 |
| C3×#815 | 2 |
| C3×#441 | 3 |
| #5184 | 3 |