Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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×D3×Q16 | C2 | semidirect |
| 4. C3×#467 | C2 | semidirect |
| 5. #5188 | C2 | semidirect |
| 6. #5116 | C2 | semidirect |
| 7. #5052 | C2 | semidirect |
| 8. #4887 | C2 | semidirect |
| 9. #4880 | C2 | semidirect |
| 10. #4816 | C2 | semidirect |
| 11. #4802 | C2 | semidirect |
| 50. #467 | D3 | semidirect |
| 268. C3 | #3059 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q16 | 2 |
| C2×#901 | 2 |
| #5628 | 2 |
| C3×#467 | 2 |
| #5188 | 2 |
| #5116 | 2 |
| #5052 | 2 |
| #4887 | 2 |
| #4880 | 2 |
| #4816 | 2 |
| #4802 | 2 |
| #3059 | 3 |