Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
326 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 66 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×#3753 | C2 | semidirect |
| 2. C3×#936 | C2 | semidirect |
| 3. C2×C3×#213 | C2 | semidirect |
| 4. #63911 | C2 | semidirect |
| 5. C2×#3717 | C2 | semidirect |
| 6. C2×#3715 | C2 | semidirect |
| 7. #63554 | C2 | semidirect |
| 28. #936 | D3 | semidirect |
| 33. C2×#213 | D3 | semidirect |
| 53. C3⋊(C3⋊C8) | D4 | semidirect |
| 54. C3×C3⋊C8 | D4 | semidirect |
| 145. C3⋊C8 | #67 | semidirect |
| 193. C32 | #496 | semidirect |
| 237. C3 | #5058 | semidirect |
| 238. C3 | #5154 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3753 | 2 |
| C3×#936 | 2 |
| C2×C3×#213 | 2 |
| #63911 | 2 |
| C2×#3717 | 2 |
| C2×#3715 | 2 |
| #63554 | 2 |
| #5154 | 3 |
| #5058 | 3 |