Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
341 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 94 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. C22×C3×Dic6 | C2 | semidirect |
| 3. C2×C3×#204 | C2 | semidirect |
| 4. C32×C22⋊C8 | C2 | semidirect |
| 5. C3×#816 | C2 | semidirect |
| 7. #4738 | C3 | direct (N × H) |
| 20. C22×Dic6 | C2×C3 | semidirect |
| 24. C2×#204 | C2×C3 | semidirect |
| 27. C3×C22⋊C8 | D3 | semidirect |
| 28. C3×C22⋊C8 | C2×C3 | semidirect |
| 29. #816 | C2×C3 | semidirect |
| 42. C3×Dic6 | D4 | semidirect |
| 71. C22×C32 | SD16 | semidirect |
| 84. C22⋊C8 | C3×D3 | semidirect |
| 114. Dic6 | C3×D4 | semidirect |
| 145. C22×C3 | #204 | semidirect |
| 146. C22×C3 | C3×SD16 | semidirect |
| 162. C32 | #448 | semidirect |
| 196. C22 | C3×#204 | semidirect |
| 203. C3 | #4738 | direct (N × H) |
| 204. C3 | C3×#448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Dic6 | 2 |
| C3×#930 | 2 |
| C2×C3×#204 | 2 |
| C32×C22⋊C8 | 2 |
| C3×#816 | 2 |
| C3×#448 | 3 |
| #4738 | 3 |