Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
224 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. C2×D3×C16 | C2 | semidirect |
| 3. D3×#108 | C2 | semidirect |
| 4. C3×#359 | C2 | semidirect |
| 5. #4567 | C2 | semidirect |
| 6. #4510 | C2 | semidirect |
| 7. #4497 | C2 | semidirect |
| 21. C2×C3×C16 | C22 | semidirect |
| 22. C3×#108 | C22 | semidirect |
| 24. #819 | C22 | semidirect |
| 25. C2×C3⋊C16 | C22 | semidirect |
| 34. #359 | D3 | direct (N × H) |
| 83. C2×C16 | C2×D3 | semidirect |
| 86. #108 | C2×D3 | semidirect |
| 196. D3 | #359 | direct (N × H) |
| 210. C3 | C2×#359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#135 | 2 |
| C2×D3×C16 | 2 |
| D3×#108 | 2 |
| C3×#359 | 2 |
| #4567 | 2 |
| #4510 | 2 |
| #4497 | 2 |
| C2×#359 | 3 |