Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
504 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 81 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×#342 | C2 | semidirect |
| 4. #4527 | C2 | semidirect |
| 5. #4526 | C2 | semidirect |
| 8. C22×C4×D3 | C4 | semidirect |
| 14. C2×(C2×D3)⋊C4 | C4 | semidirect |
| 20. #342 | D3 | semidirect |
| 196. C3 | #1819 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C22⋊C4 | 2 |
| #4955 | 2 |
| C3×#342 | 2 |
| #4527 | 2 |
| #4526 | 2 |
| #1819 | 3 |