Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
177 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 177 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×C3×Dic12 | C2 | semidirect |
| 3. #63639 | C2 | semidirect |
| 4. #63550 | C2 | semidirect |
| 5. #63547 | C2 | semidirect |
| 19. C2×Dic12 | D3 | semidirect |
| 120. C32 | #510 | semidirect |
| 146. C3 | #5179 | semidirect |
| 147. C3 | #5195 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic12 | 2 |
| C3×#904 | 2 |
| #63639 | 2 |
| #63550 | 2 |
| #63547 | 2 |
| #5195 | 3 |
| #5179 | 3 |