Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
253 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 253 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 |
|---|---|---|
| 2. C2×C3×C4⋊Dic3 | C2 | semidirect |
| 3. #63657 | C2 | semidirect |
| 4. #63574 | C2 | semidirect |
| 5. #63562 | C2 | semidirect |
| 20. C2×C4⋊Dic3 | D3 | semidirect |
| 145. C32 | #481 | semidirect |
| 183. C3 | #4968 | semidirect |
| 184. C3 | #5034 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#930 | 2 |
| C2×C3×C4⋊Dic3 | 2 |
| #63657 | 2 |
| #63574 | 2 |
| #63562 | 2 |
| #5034 | 3 |
| #4968 | 3 |