Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 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×C3×C4×C8 | C2 | semidirect |
| 4. C2×C8×Dic3 | C2 | semidirect |
| 6. #4550 | C2 | semidirect |
| 7. #4524 | C2 | semidirect |
| 19. C2×D3×C8 | C4 | semidirect |
| 22. (C2×D3)⋊C8 | C4 | semidirect |
| 27. C2×C4×C8 | D3 | semidirect |
| 50. (C2×D3)⋊C4 | C8 | direct (N × H) |
| 83. C2×C3×C4 | C2×C8 | semidirect |
| 95. C2×Dic3 | C2×C8 | semidirect |
| 101. C3×C8 | C22⋊C4 | semidirect |
| 142. C2×D3 | C4×C8 | semidirect |
| 168. C2×C4 | D3×C8 | semidirect |
| 178. C8 | (C2×D3)⋊C4 | direct (N × H) |
| 202. C3 | C8×C22⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×C8×Dic3 | 2 |
| C4×(C2×D3)⋊C4 | 2 |
| #4550 | 2 |
| #4524 | 2 |
| C8×C22⋊C4 | 3 |