Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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×#462 | C2 | semidirect |
| 5. #5184 | C2 | semidirect |
| 6. #5090 | C2 | semidirect |
| 7. #5020 | C2 | semidirect |
| 8. #4851 | C2 | semidirect |
| 11. #4789 | C2 | semidirect |
| 50. #462 | D3 | semidirect |
| 260. C3 | #3113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| C4×D3×Q8 | 2 |
| C3×#462 | 2 |
| #5186 | 2 |
| #5184 | 2 |
| #5090 | 2 |
| #5020 | 2 |
| #4851 | 2 |
| #4835 | 2 |
| #4805 | 2 |
| #4789 | 2 |
| #3113 | 3 |