Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 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 |
|---|---|---|
| 1. #5728 | C2 | semidirect |
| 3. C3×#461 | C2 | semidirect |
| 4. #5171 | C2 | semidirect |
| 5. #5163 | C2 | semidirect |
| 6. #5083 | C2 | semidirect |
| 7. #5008 | C2 | semidirect |
| 8. #4842 | C2 | semidirect |
| 9. D3×C4⋊C8 | C2 | semidirect |
| 10. #4807 | C2 | semidirect |
| 11. #4791 | C2 | semidirect |
| 52. #461 | D3 | semidirect |
| 153. C4×D3 | SD16 | semidirect |
| 278. C3 | #3246 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5728 | 2 |
| #5548 | 2 |
| C3×#461 | 2 |
| #5171 | 2 |
| #5163 | 2 |
| #5083 | 2 |
| #5008 | 2 |
| #4842 | 2 |
| D3×C4⋊C8 | 2 |
| #4807 | 2 |
| #4791 | 2 |
| #3246 | 3 |