Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 2. #5470 | C2 | semidirect |
| 3. C2×C3×C4×C8 | C2 | semidirect |
| 4. #5114 | C2 | semidirect |
| 5. #4694 | C2 | semidirect |
| 6. #4693 | C2 | semidirect |
| 7. C4×#204 | C2 | semidirect |
| 8. #4681 | C2 | semidirect |
| 9. #4680 | C2 | semidirect |
| 44. C2×C4×C8 | D3 | semidirect |
| 106. C2×C3×C4 | SD16 | semidirect |
| 125. C3×C8 | #41 | semidirect |
| 189. C2×C4 | #204 | semidirect |
| 197. C8 | #235 | semidirect |
| 219. C3 | #3167 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| #5470 | 2 |
| C2×C3×C4×C8 | 2 |
| #5114 | 2 |
| #4694 | 2 |
| #4693 | 2 |
| C4×#204 | 2 |
| #4681 | 2 |
| #4680 | 2 |
| #3167 | 3 |