Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
341 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 80 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. C22×C3×Dic6 | C2 | semidirect |
| 3. C2×#3715 | C2 | semidirect |
| 4. #63657 | C2 | semidirect |
| 5. #63565 | C2 | semidirect |
| 20. C22×Dic6 | D3 | semidirect |
| 42. C3×Dic6 | D4 | semidirect |
| 71. C22×C32 | SD16 | semidirect |
| 114. Dic6 | #67 | semidirect |
| 145. C22×C3 | #214 | semidirect |
| 146. C22×C3 | #215 | semidirect |
| 162. C32 | #448 | semidirect |
| 196. C22 | #3715 | semidirect |
| 203. C3 | #5040 | semidirect |
| 204. C3 | #5227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic6 | 2 |
| C3×#930 | 2 |
| C2×#3715 | 2 |
| #63657 | 2 |
| #63565 | 2 |
| #5227 | 3 |
| #5040 | 3 |