Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
140 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 58 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×Dic6 | C2 | semidirect |
| 3. C3×#216 | C2 | semidirect |
| 4. C3×#214 | C2 | semidirect |
| 5. C3×#208 | C2 | semidirect |
| 7. #951 | C3 | direct (N × H) |
| 21. C2×Dic6 | C2×C3 | semidirect |
| 25. #216 | C2×C3 | semidirect |
| 26. #214 | C2×C3 | semidirect |
| 27. #208 | C2×C3 | semidirect |
| 83. C32 | #137 | semidirect |
| 109. C3 | #951 | direct (N × H) |
| 110. C3 | C3×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#41 | 2 |
| C2×C3×Dic6 | 2 |
| C3×#216 | 2 |
| C3×#214 | 2 |
| C3×#208 | 2 |
| C3×#137 | 3 |
| #951 | 3 |