Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
564 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 373 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. #4997 | C2 | semidirect |
| 4. C4×#208 | C2 | semidirect |
| 12. C2×#208 | C4 | semidirect |
| 16. #803 | C22 | semidirect |
| 17. C4×C3⋊C8 | C22 | semidirect |
| 34. #208 | C2×C4 | semidirect |
| 35. C2×C3⋊C8 | C2×C4 | semidirect |
| 118. C3 | #2873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#117 | 2 |
| C22×#208 | 2 |
| #4997 | 2 |
| C4×#208 | 2 |
| #2873 | 3 |