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 |
|---|---|---|
| 1. #5580 | C2 | semidirect |
| 2. C3×C4×Q16 | C2 | semidirect |
| 3. #5191 | C2 | semidirect |
| 4. #5188 | C2 | semidirect |
| 5. C4×#215 | C2 | semidirect |
| 7. #4878 | C2 | semidirect |
| 8. #4807 | C2 | semidirect |
| 9. #4800 | C2 | semidirect |
| 10. C4×D24 | C2 | semidirect |
| 11. C4×D3×C8 | C2 | semidirect |
| 47. C4×Q16 | D3 | semidirect |
| 231. C3 | #3168 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5580 | 2 |
| C3×C4×Q16 | 2 |
| #5191 | 2 |
| #5188 | 2 |
| C4×#215 | 2 |
| #4883 | 2 |
| #4878 | 2 |
| #4807 | 2 |
| #4800 | 2 |
| C4×D24 | 2 |
| C4×D3×C8 | 2 |
| #3168 | 3 |