Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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×C22⋊C8 | C2 | semidirect |
| 3. C2×#830 | C2 | semidirect |
| 4. #4468 | C2 | direct (N × H) |
| 18. C3×C22⋊C8 | C22 | semidirect |
| 20. #830 | C22 | semidirect |
| 23. C2×C22⋊C8 | D3 | semidirect |
| 31. C23×D3 | C8 | semidirect |
| 66. C22⋊C8 | C2×D3 | semidirect |
| 86. C22×D3 | C2×C8 | semidirect |
| 194. C2×C3 | #323 | semidirect |
| 224. C3 | C2×#323 | semidirect |
| 229. C2 | #4468 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D3)⋊C4 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#830 | 2 |
| #4468 | 2 |
| C2×#323 | 3 |