Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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×C3×AGL(1,ℤ/8) | C2 | semidirect |
| 2. C2×#949 | C2 | semidirect |
| 3. C22×#213 | C2 | semidirect |
| 4. #5234 | C2 | semidirect |
| 5. C2×#833 | C2 | semidirect |
| 6. C2×#823 | C2 | semidirect |
| 7. #4558 | C2 | semidirect |
| 31. C2×AGL(1,ℤ/8) | D3 | semidirect |
| 257. C3 | #2018 | 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 |
| C2×#949 | 2 |
| C22×#213 | 2 |
| #5234 | 2 |
| C2×#833 | 2 |
| C2×#823 | 2 |
| #4558 | 2 |
| #2018 | 3 |