Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
424 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 3. C3×#340 | C2 | semidirect |
| 4. #4551 | C2 | semidirect |
| 5. #4529 | C2 | semidirect |
| 15. C2×D3×C8 | C4 | semidirect |
| 17. #892 | C4 | semidirect |
| 22. #340 | D3 | semidirect |
| 158. C3 | #1735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×C8 | 2 |
| C2×#892 | 2 |
| C3×#340 | 2 |
| #4551 | 2 |
| #4529 | 2 |
| #1735 | 3 |