Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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. Dic3×M16 | C2 | semidirect |
| 4. C3×#343 | C2 | semidirect |
| 5. #4530 | C2 | semidirect |
| 16. #823 | C4 | semidirect |
| 23. #343 | D3 | semidirect |
| 37. C3×M16 | C2×C4 | semidirect |
| 44. #208 | C2×C4 | semidirect |
| 96. M16 | C4×D3 | semidirect |
| 118. Dic3 | #100 | semidirect |
| 164. C3 | C4×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#893 | 2 |
| C2×#823 | 2 |
| Dic3×M16 | 2 |
| C3×#343 | 2 |
| #4530 | 2 |
| C4×#100 | 3 |