Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
228 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 85 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. #5106 | C2 | semidirect |
| 4. #4509 | C2 | semidirect |
| 5. #4503 | C2 | semidirect |
| 12. #904 | C4 | semidirect |
| 20. C22×C16 | D3 | semidirect |
| 134. C3 | #2138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#904 | 2 |
| C22×C3×C16 | 2 |
| #5106 | 2 |
| #4509 | 2 |
| #4503 | 2 |
| #2138 | 3 |