Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. C3×#441 | C2 | semidirect |
| 4. #5184 | C2 | semidirect |
| 5. C4×#216 | C2 | semidirect |
| 7. #4853 | C2 | semidirect |
| 9. #4790 | C2 | semidirect |
| 10. #4716 | C2 | semidirect |
| 18. D3×Q16 | C4 | semidirect |
| 46. #441 | D3 | semidirect |
| 213. C3 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q16 | 2 |
| #5572 | 2 |
| C3×#441 | 2 |
| #5184 | 2 |
| C4×#216 | 2 |
| #4860 | 2 |
| #4853 | 2 |
| #4802 | 2 |
| #4790 | 2 |
| #4716 | 2 |
| #4708 | 2 |
| #2950 | 3 |