Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 612 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. C2×C3×#99 | C2 | semidirect |
| 3. C2×#834 | C2 | semidirect |
| 4. C2×#806 | C2 | semidirect |
| 5. #4943 | C2 | semidirect |
| 8. C22×#67 | C4 | semidirect |
| 10. C23×Dic3 | C4 | semidirect |
| 16. C22×C4×D3 | C4 | semidirect |
| 17. C22×Dic6 | C4 | semidirect |
| 27. C2×#99 | D3 | semidirect |
| 260. C3 | #1782 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#237 | 2 |
| C2×C3×#99 | 2 |
| C2×#834 | 2 |
| C2×#806 | 2 |
| #4943 | 2 |
| #1782 | 3 |