Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
438 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 57 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. D3×#100 | C2 | semidirect |
| 3. D3×#99 | C2 | semidirect |
| 4. C3×AΣL(1,𝔽16) | C2 | semidirect |
| 5. #4536 | C2 | semidirect |
| 6. #4475 | C2 | semidirect |
| 7. #4471 | C2 | semidirect |
| 9. C24×D3 | C4 | semidirect |
| 13. #953 | C4 | semidirect |
| 18. #882 | C4 | semidirect |
| 21. D3×C22⋊C4 | C4 | semidirect |
| 22. C3×#100 | C22 | semidirect |
| 23. C3×#99 | C22 | semidirect |
| 24. #834 | C22 | semidirect |
| 25. #833 | C22 | semidirect |
| 34. AΣL(1,𝔽16) | D3 | direct (N × H) |
| 35. C24×C3 | C2×C4 | semidirect |
| 42. C23×D3 | C2×C4 | semidirect |
| 61. C3×C22⋊C4 | C2×C4 | semidirect |
| 64. #217 | C2×C4 | semidirect |
| 87. #100 | C2×D3 | semidirect |
| 90. #99 | C2×D3 | semidirect |
| 147. C24 | C4×D3 | semidirect |
| 175. C22⋊C4 | C4×D3 | semidirect |
| 268. D3 | AΣL(1,𝔽16) | direct (N × H) |
| 304. C3 | C2×AΣL(1,𝔽16) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#120 | 2 |
| D3×#100 | 2 |
| D3×#99 | 2 |
| C3×AΣL(1,𝔽16) | 2 |
| #4536 | 2 |
| #4475 | 2 |
| #4471 | 2 |
| C2×AΣL(1,𝔽16) | 3 |