Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
363 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 363 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 |
|---|---|---|
| 1. C2×#3797 | C2 | semidirect |
| 3. C2×#3717 | C2 | semidirect |
| 4. C3×#810 | C2 | semidirect |
| 5. #63557 | C2 | semidirect |
| 25. #810 | D3 | semidirect |
| 36. C3×Dic6 | D4 | semidirect |
| 67. C2×C3⋊D3 | SD16 | semidirect |
| 102. Dic6 | D12 | semidirect |
| 144. C32 | #448 | semidirect |
| 181. C3 | #4806 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3797 | 2 |
| #64104 | 2 |
| C2×#3717 | 2 |
| C3×#810 | 2 |
| #63557 | 2 |
| #4806 | 3 |