Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 1. C2×#800 | C2 | semidirect |
| 3. #4696 | C2 | semidirect |
| 4. C4×D24 | C2 | semidirect |
| 5. C3×C4⋊C16 | C2 | semidirect |
| 6. #4509 | C2 | semidirect |
| 7. #4503 | C2 | semidirect |
| 26. C4⋊C16 | D3 | semidirect |
| 147. C3 | #2210 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#800 | 2 |
| C2×D48 | 2 |
| #4696 | 2 |
| C4×D24 | 2 |
| C3×C4⋊C16 | 2 |
| #4509 | 2 |
| #4503 | 2 |
| #2210 | 3 |