Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
141 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 141 conjugacy classes of subgroups — too many to draw. Only its 54 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. C22×Dic9 | C2 | semidirect |
| 3. C2×C4×D9 | C2 | semidirect |
| 4. C9×C22⋊C4 | C2 | semidirect |
| 5. (C2×D9)⋊C4 | C2 | semidirect |
| 6. Dic9⋊C4 | C2 | semidirect |
| 7. C4×Dic9 | C2 | semidirect |
| 13. #611 | C4 | semidirect |
| 28. C22×C9 | C2×C4 | semidirect |
| 32. C2×D9 | C2×C4 | semidirect |
| 36. Dic9 | C2×C4 | semidirect |
| 37. Dic9 | D4 | semidirect |
| 59. C22⋊C4 | D9 | semidirect |
| 73. C9 | C4×D4 | semidirect |
| 94. C22 | C4×D9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#611 | 2 |
| C22×Dic9 | 2 |
| C2×C4×D9 | 2 |
| C9×C22⋊C4 | 2 |
| (C2×D9)⋊C4 | 2 |
| Dic9⋊C4 | 2 |
| C4×Dic9 | 2 |
| #67⋊C4 | 3 |