Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
272 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 101 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. C22×C3×C16 | C2 | semidirect |
| 3. C2×#818 | C2 | semidirect |
| 4. #4509 | C2 | direct (N × H) |
| 11. C2×D24 | C4 | semidirect |
| 14. C2×C3×C16 | C22 | semidirect |
| 16. #818 | C22 | semidirect |
| 18. C22×C16 | D3 | semidirect |
| 36. D24 | C2×C4 | semidirect |
| 46. C2×C16 | C2×D3 | semidirect |
| 112. C2×C3 | #357 | semidirect |
| 129. C3 | C2×#357 | semidirect |
| 131. C2 | #4509 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D24 | 2 |
| C22×C3×C16 | 2 |
| C2×#818 | 2 |
| #4509 | 2 |
| C2×#357 | 3 |