Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
238 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 72 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 |
|---|---|---|
| 3. C3×#819 | C2 | semidirect |
| 4. #63578 | C2 | semidirect |
| 18. #819 | D3 | semidirect |
| 88. C32 | #430 | semidirect |
| 110. C3 | #4893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3743 | 2 |
| #63818 | 2 |
| C3×#819 | 2 |
| #63578 | 2 |
| #4893 | 3 |