Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
364 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5563 | C2 | semidirect |
| 2. C3×C8×D4 | C2 | semidirect |
| 3. #5115 | C2 | semidirect |
| 4. #5106 | C2 | semidirect |
| 5. #4842 | C2 | semidirect |
| 6. #4737 | C2 | semidirect |
| 7. C4×D24 | C2 | semidirect |
| 8. #4682 | C2 | semidirect |
| 35. C8×D4 | D3 | semidirect |
| 169. C3 | #3341 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5563 | 2 |
| C3×C8×D4 | 2 |
| #5115 | 2 |
| #5106 | 2 |
| #4842 | 2 |
| #4737 | 2 |
| C4×D24 | 2 |
| #4682 | 2 |
| #3341 | 3 |