Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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. D3×C4⋊Q8 | C2 | semidirect |
| 4. C3×#462 | C2 | semidirect |
| 5. #5182 | C2 | semidirect |
| 6. #5083 | C2 | semidirect |
| 7. #5031 | C2 | semidirect |
| 8. #4841 | C2 | semidirect |
| 9. #4837 | C2 | semidirect |
| 10. #4818 | C2 | semidirect |
| 11. #4802 | C2 | semidirect |
| 50. #462 | D3 | semidirect |
| 220. C3×C4 | #137 | semidirect |
| 227. Dic3 | #137 | semidirect |
| 282. C4 | #918 | semidirect |
| 285. C3 | #3039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#918 | 2 |
| D3×C4⋊Q8 | 2 |
| C4×#239 | 2 |
| C3×#462 | 2 |
| #5182 | 2 |
| #5083 | 2 |
| #5031 | 2 |
| #4841 | 2 |
| #4837 | 2 |
| #4818 | 2 |
| #4802 | 2 |
| #3039 | 3 |