Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 117 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×#817 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 7. #4929 | C2 | semidirect |
| 19. C2×#204 | C4 | semidirect |
| 29. C2×C4×C8 | D3 | semidirect |
| 88. C2×C3×C4 | SD16 | semidirect |
| 111. C3×C8 | C22⋊C4 | semidirect |
| 185. C2×C4 | #204 | semidirect |
| 193. C8 | (C2×D3)⋊C4 | semidirect |
| 218. C3 | #1968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C2×C3×C4×C8 | 2 |
| C2×#821 | 2 |
| C2×#817 | 2 |
| C2×#816 | 2 |
| #4939 | 2 |
| #4929 | 2 |
| #1968 | 3 |