Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
402 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 133 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. C3×C4×M16 | C2 | semidirect |
| 4. #5134 | C2 | semidirect |
| 5. #4710 | C2 | semidirect |
| 6. #4694 | C2 | semidirect |
| 7. #4693 | C2 | semidirect |
| 8. #4682 | C2 | semidirect |
| 9. #4681 | C2 | semidirect |
| 44. C4×M16 | D3 | semidirect |
| 125. C3×C8 | #41 | semidirect |
| 197. C8 | #235 | semidirect |
| 219. C3 | #3182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5477 | 2 |
| #5470 | 2 |
| C3×C4×M16 | 2 |
| #5134 | 2 |
| #4710 | 2 |
| #4694 | 2 |
| #4693 | 2 |
| #4682 | 2 |
| #4681 | 2 |
| #3182 | 3 |