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. C2×#870 | C2 | semidirect |
| 3. C2×C3×C4×C8 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 6. #4697 | C2 | direct (N × H) |
| 18. #870 | C22 | semidirect |
| 19. C3×C4×C8 | C22 | semidirect |
| 21. #816 | C22 | semidirect |
| 27. C2×C4×C8 | D3 | semidirect |
| 60. C4×C8 | C2×D3 | semidirect |
| 127. C2×C3 | #488 | semidirect |
| 142. C3 | C2×#488 | semidirect |
| 144. C2 | #4697 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#875 | 2 |
| C2×#870 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×#821 | 2 |
| C2×#816 | 2 |
| #4697 | 2 |
| C2×#488 | 3 |