Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
318 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. C2×#816 | C2 | semidirect |
| 5. C2×#816 | C2 | semidirect |
| 6. #4928 | C2 | semidirect |
| 7. C3×#336 | C2 | semidirect |
| 32. #336 | D3 | semidirect |
| 250. C3 | #2042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#875 | 2 |
| C2×#821 | 2 |
| C2×#816 | 2 |
| #4928 | 2 |
| C3×#336 | 2 |
| #2042 | 3 |