Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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×Q32 | C2 | semidirect |
| 4. C2×#829 | C2 | semidirect |
| 5. #4564 | C2 | semidirect |
| 7. #4503 | C2 | semidirect |
| 26. C2×Q32 | D3 | semidirect |
| 117. C2×D3 | Q32 | semidirect |
| 160. C3 | #2188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q16 | 2 |
| C2×C3×Q32 | 2 |
| #5188 | 2 |
| C2×#829 | 2 |
| #4564 | 2 |
| (C2×D3)⋊C16 | 2 |
| #4503 | 2 |
| #2188 | 3 |