Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 4. C2×#818 | C2 | semidirect |
| 5. C2×#817 | C2 | semidirect |
| 6. C2×#816 | C2 | semidirect |
| 7. C2×#816 | C2 | semidirect |
| 8. #4723 | C2 | direct (N × H) |
| 26. #818 | C22 | semidirect |
| 27. #817 | C22 | semidirect |
| 28. #816 | C22 | semidirect |
| 29. #816 | C22 | semidirect |
| 187. C2×C3 | #485 | semidirect |
| 207. C3 | C2×#485 | semidirect |
| 209. C2 | #4723 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#926 | 2 |
| C2×#924 | 2 |
| C2×C3×C22⋊C8 | 2 |
| C2×#818 | 2 |
| C2×#817 | 2 |
| C2×#816 | 2 |
| #4723 | 2 |
| C2×#485 | 3 |