Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
295 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 295 conjugacy classes of subgroups — too many to draw. Only its 84 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. C22×C3×C3⋊C8 | C2 | semidirect |
| 3. C2×#3712 | C2 | semidirect |
| 4. C3×#830 | C2 | semidirect |
| 5. #63572 | C2 | semidirect |
| 6. #63557 | C2 | semidirect |
| 7. #63555 | C2 | semidirect |
| 27. C22×C3⋊C8 | D3 | semidirect |
| 31. #830 | D3 | semidirect |
| 53. C3×C3⋊C8 | D4 | semidirect |
| 90. C22×C32 | M16 | semidirect |
| 151. C3⋊C8 | #67 | semidirect |
| 178. C22×C3 | ΓL(1,𝔽25) | semidirect |
| 179. C22×C3 | ΓL(1,𝔽25) | semidirect |
| 209. C32 | #435 | semidirect |
| 246. C22 | #3712 | semidirect |
| 255. C3 | #4730 | semidirect |
| 256. C3 | #5111 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#638 | 2 |
| C22×C3×C3⋊C8 | 2 |
| C2×#3712 | 2 |
| C3×#830 | 2 |
| #63572 | 2 |
| #63557 | 2 |
| #63555 | 2 |
| #5111 | 3 |
| #4730 | 3 |