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×#461 | C2 | semidirect |
| 5. #5162 | C2 | semidirect |
| 6. #5090 | C2 | semidirect |
| 7. #5019 | C2 | semidirect |
| 8. #4849 | C2 | semidirect |
| 9. #4837 | C2 | semidirect |
| 10. #4802 | C2 | semidirect |
| 11. #4795 | C2 | semidirect |
| 53. #461 | D3 | semidirect |
| 219. C3×C4 | #137 | semidirect |
| 227. Dic3 | #137 | semidirect |
| 282. C4 | #915 | 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×#915 | 2 |
| D3×C4⋊Q8 | 2 |
| C4×#237 | 2 |
| C3×#461 | 2 |
| #5162 | 2 |
| #5090 | 2 |
| #5019 | 2 |
| #4849 | 2 |
| #4837 | 2 |
| #4802 | 2 |
| #4795 | 2 |
| #3039 | 3 |