Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
386 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 68 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 |
|---|---|---|
| 2. C2×C3×#216 | C2 | semidirect |
| 3. #63871 | C2 | semidirect |
| 4. C2×#3717 | C2 | semidirect |
| 5. C3×#835 | C2 | semidirect |
| 6. #63564 | C2 | semidirect |
| 7. #63557 | C2 | semidirect |
| 30. C2×#216 | D3 | semidirect |
| 35. #835 | D3 | semidirect |
| 225. C32 | #452 | semidirect |
| 274. C3 | #4808 | semidirect |
| 275. C3 | #5187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3832 | 2 |
| C2×C3×#216 | 2 |
| #63871 | 2 |
| C2×#3717 | 2 |
| C3×#835 | 2 |
| #63564 | 2 |
| #63557 | 2 |
| #5187 | 3 |
| #4808 | 3 |