Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 3. #4973 | C2 | semidirect |
| 4. C2×#810 | C2 | semidirect |
| 6. C3×#340 | C2 | semidirect |
| 7. #4550 | C2 | semidirect |
| 20. C2×#204 | C4 | semidirect |
| 32. #340 | D3 | semidirect |
| 55. C2×Dic6 | C2×C4 | semidirect |
| 58. C2×C3×C8 | C2×C4 | semidirect |
| 116. C2×Dic3 | SD16 | semidirect |
| 156. C2×C8 | C4×D3 | semidirect |
| 258. C3 | #1877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#204 | 2 |
| C2×#893 | 2 |
| #4973 | 2 |
| C2×#810 | 2 |
| C2×#809 | 2 |
| C3×#340 | 2 |
| #4550 | 2 |
| #1877 | 3 |