Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
220 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 47 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. #5757 | C2 | semidirect |
| 2. C2×C3×D16 | C2 | semidirect |
| 3. #5160 | C2 | semidirect |
| 4. #5147 | C2 | semidirect |
| 5. #4563 | C2 | semidirect |
| 6. #4510 | C2 | semidirect |
| 7. #4508 | C2 | semidirect |
| 11. C2×C3×D8 | C22 | semidirect |
| 20. C2×C3×C16 | C22 | semidirect |
| 24. #819 | C22 | semidirect |
| 25. #812 | C22 | semidirect |
| 28. C2×D16 | D3 | semidirect |
| 68. C2×D8 | C2×D3 | semidirect |
| 74. C2×C16 | C2×D3 | semidirect |
| 180. C3 | #2192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5757 | 2 |
| C2×C3×D16 | 2 |
| #5160 | 2 |
| #5147 | 2 |
| #4563 | 2 |
| #4510 | 2 |
| #4508 | 2 |
| #2192 | 3 |