Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×C3×#137 | C2 | semidirect |
| 2. #5827 | C2 | semidirect |
| 4. #5816 | C2 | semidirect |
| 5. C2×#835 | C2 | semidirect |
| 6. #5185 | C2 | semidirect |
| 7. #5182 | C2 | semidirect |
| 8. #5165 | C2 | semidirect |
| 9. #5162 | C2 | semidirect |
| 10. #5133 | C2 | semidirect |
| 11. #5119 | C2 | semidirect |
| 44. C2×#137 | D3 | semidirect |
| 286. C3 | #3046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#137 | 2 |
| #5827 | 2 |
| C2×#950 | 2 |
| #5816 | 2 |
| C2×#835 | 2 |
| #5185 | 2 |
| #5182 | 2 |
| #5165 | 2 |
| #5162 | 2 |
| #5133 | 2 |
| #5119 | 2 |
| #3046 | 3 |