Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
154 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 53 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. C3×#442 | C2 | semidirect |
| 3. #4717 | C2 | semidirect |
| 4. #4563 | C2 | semidirect |
| 5. #4488 | C2 | semidirect |
| 6. #4487 | C2 | semidirect |
| 7. #4466 | C2 | semidirect |
| 16. #827 | C4 | semidirect |
| 17. #826 | C4 | semidirect |
| 24. #442 | D3 | semidirect |
| 40. Dic12 | C2×C4 | semidirect |
| 41. D24 | C2×C4 | semidirect |
| 46. C3⋊C16 | C2×C4 | semidirect |
| 132. C3 | AGL(1,ℤ/16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#442 | 2 |
| #5147 | 2 |
| #4717 | 2 |
| #4563 | 2 |
| #4488 | 2 |
| #4487 | 2 |
| #4466 | 2 |
| AGL(1,ℤ/16) | 3 |