Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
230 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 230 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. C2×#904 | C2 | semidirect |
| 2. C3×#466 | C2 | semidirect |
| 3. C2×#827 | C2 | semidirect |
| 4. C2×#826 | C2 | semidirect |
| 5. #4549 | C2 | semidirect |
| 6. #4492 | C2 | semidirect |
| 7. #4491 | C2 | semidirect |
| 27. #466 | D3 | semidirect |
| 49. Dic12 | D4 | semidirect |
| 51. D24 | D4 | semidirect |
| 172. C3 | #2186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| C3×#466 | 2 |
| C2×#827 | 2 |
| C2×#826 | 2 |
| #4549 | 2 |
| #4492 | 2 |
| #4491 | 2 |
| #2186 | 3 |