Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 119 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. Dic3×M16 | C2 | semidirect |
| 5. #4554 | C2 | semidirect |
| 16. C3×#100 | C4 | semidirect |
| 17. #833 | C4 | semidirect |
| 38. C3×M16 | C2×C4 | semidirect |
| 45. #208 | C2×C4 | semidirect |
| 57. #100 | Dic3 | direct (N × H) |
| 98. M16 | C2×Dic3 | semidirect |
| 120. Dic3 | #100 | direct (N × H) |
| 166. C3 | C4×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic3 | 2 |
| C2×C3×#100 | 2 |
| C2×#833 | 2 |
| Dic3×M16 | 2 |
| #4554 | 2 |
| C4×#100 | 3 |