Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
460 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 165 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. #4971 | C2 | direct (N × H) |
| 5. C2×#810 | C2 | semidirect |
| 6. C2×#808 | C2 | semidirect |
| 22. #810 | C22 | semidirect |
| 23. #808 | C22 | semidirect |
| 151. C2×C3 | #483 | semidirect |
| 169. C3 | C2×#483 | semidirect |
| 171. C2 | #4971 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4⋊C4 | 2 |
| C2×#924 | 2 |
| C2×#830 | 2 |
| #4971 | 2 |
| C2×#810 | 2 |
| C2×#808 | 2 |
| C2×#483 | 3 |