Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
282 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 87 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×C3⋊Dic3 | C2 | semidirect |
| 3. C2×C4×C3⋊D3 | C2 | semidirect |
| 4. C32×C22⋊C4 | C2 | semidirect |
| 5. #3752 | C2 | semidirect |
| 6. #3750 | C2 | semidirect |
| 7. C4×C3⋊Dic3 | C2 | semidirect |
| 13. #638 | C4 | semidirect |
| 22. C3×C22⋊C4 | D3 | semidirect |
| 28. C22×C32 | C2×C4 | semidirect |
| 32. C2×C3⋊D3 | C2×C4 | semidirect |
| 36. C3⋊Dic3 | C2×C4 | semidirect |
| 37. C3⋊Dic3 | D4 | semidirect |
| 59. C22⋊C4 | C3⋊D3 | semidirect |
| 63. C22×C3 | C4×D3 | semidirect |
| 73. C32 | C4×D4 | semidirect |
| 94. C22 | C4×C3⋊D3 | semidirect |
| 101. C3 | #67⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#638 | 2 |
| C22×C3⋊Dic3 | 2 |
| C2×C4×C3⋊D3 | 2 |
| C32×C22⋊C4 | 2 |
| #3752 | 2 |
| #3750 | 2 |
| C4×C3⋊Dic3 | 2 |
| #67⋊C4 | 3 |