Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 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. #5237 | C2 | semidirect |
| 3. #5236 | C2 | semidirect |
| 4. C2×#833 | C2 | semidirect |
| 5. #5215 | C2 | semidirect |
| 6. #5124 | C2 | semidirect |
| 7. #4559 | C2 | semidirect |
| 214. C3 | #2048 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×AGL(1,ℤ/8) | 2 |
| #5237 | 2 |
| #5236 | 2 |
| C2×#833 | 2 |
| #5215 | 2 |
| #5124 | 2 |
| #4559 | 2 |
| #2048 | 3 |