Finite Group DatabasebetaFinite Group DatabasebetaOrder 288.
167 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 167 conjugacy classes of subgroups — too many to draw. Only its 70 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. C2×C32×Q8 | C2 | semidirect |
| 4. C3×C4⋊Dic3 | C2 | semidirect |
| 5. C3×Dic3⋊C4 | C2 | semidirect |
| 7. #946 | C3 | direct (N × H) |
| 16. C2×C3×Q8 | D3 | semidirect |
| 17. C2×C3×Q8 | C2×C3 | semidirect |
| 24. C4⋊Dic3 | C2×C3 | semidirect |
| 25. Dic3⋊C4 | C2×C3 | semidirect |
| 29. C2×C3×D3 | Q8 | semidirect |
| 56. C2×Q8 | C3×D3 | semidirect |
| 69. C2×D3 | C3×Q8 | semidirect |
| 80. C32 | C22⋊Q8 | semidirect |
| 108. C3 | #946 | direct (N × H) |
| 109. C3 | C3×C22⋊Q8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×Q8 | 2 |
| C2×C3×C4×D3 | 2 |
| C3×(C2×D3)⋊C4 | 2 |
| C3×C4⋊Dic3 | 2 |
| C3×Dic3⋊C4 | 2 |
| C3×C22⋊Q8 | 3 |
| #946 | 3 |