Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
127 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 127 conjugacy classes of subgroups — too many to draw. Only its 40 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. C3×C4⋊Dic3 | C2 | semidirect |
| 3. C2×C3×C3⋊C8 | C2 | semidirect |
| 9. C4⋊(C3⋊D3) | C4 | semidirect |
| 17. C4⋊Dic3 | D3 | semidirect |
| 18. C2×C3⋊C8 | D3 | semidirect |
| 70. C32 | #102 | semidirect |
| 97. C3 | #809 | semidirect |
| 98. C3 | #821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D3) | 2 |
| C3×C4⋊Dic3 | 2 |
| C2×C3×C3⋊C8 | 2 |
| #821 | 3 |
| #809 | 3 |