Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
326 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 4. C3×#824 | C2 | direct (N × H) |
| 6. C2×#824 | C3 | direct (N × H) |
| 29. #824 | C2×C3 | direct (N × H) |
| 134. C2×C32 | #101 | semidirect |
| 176. C32 | C2×#101 | semidirect |
| 201. C2×C3 | #824 | direct (N × H) |
| 202. C2×C3 | C3×#101 | semidirect |
| 215. C3 | C2×#824 | direct (N × H) |
| 216. C3 | C2×C3×#101 | semidirect |
| 219. C2 | C3×#824 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic6 | 2 |
| C2×C32×M16 | 2 |
| C2×C3×#208 | 2 |
| C3×#824 | 2 |
| C2×C3×#101 | 3 |
| C2×#824 | 3 |