Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
194 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 56 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×#3746 | C2 | semidirect |
| 3. C3×#812 | C2 | semidirect |
| 4. #63551 | C2 | semidirect |
| 5. #63548 | C2 | semidirect |
| 25. #812 | D3 | semidirect |
| 126. C32 | #510 | semidirect |
| 152. C3 | #4909 | semidirect |
| 153. C3 | #5195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3746 | 2 |
| C3×#904 | 2 |
| C3×#812 | 2 |
| #63551 | 2 |
| #63548 | 2 |
| #5195 | 3 |
| #4909 | 3 |