Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C22×C3×D8 | C2 | semidirect |
| 2. #5806 | C2 | semidirect |
| 3. C2×#912 | C2 | semidirect |
| 4. #5218 | C2 | semidirect |
| 5. #5158 | C2 | semidirect |
| 6. #5157 | C2 | semidirect |
| 7. #5155 | C2 | semidirect |
| 8. #5153 | C2 | semidirect |
| 9. Dic3×D8 | C2 | semidirect |
| 10. #5116 | C2 | semidirect |
| 11. C8×#67 | C2 | semidirect |
| 14. C2×#237 | C22 | semidirect |
| 23. #938 | C22 | semidirect |
| 24. #936 | C22 | semidirect |
| 26. D4×Dic3 | C22 | semidirect |
| 27. C2×#214 | C22 | semidirect |
| 28. C2×#214 | C22 | semidirect |
| 32. C2×Dic12 | C22 | semidirect |
| 33. C2×D3×C8 | C22 | semidirect |
| 34. #832 | C22 | semidirect |
| 35. #832 | C22 | semidirect |
| 37. (C2×D3)⋊C8 | C22 | semidirect |
| 38. #818 | C22 | semidirect |
| 39. #816 | C22 | semidirect |
| 40. Dic3⋊C8 | C22 | semidirect |
| 41. C8×Dic3 | C22 | semidirect |
| 43. C22×D8 | D3 | semidirect |
| 71. C3×D8 | D4 | semidirect |
| 176. D8 | #67 | semidirect |
| 203. C22×C3 | #135 | semidirect |
| 269. C22 | #912 | semidirect |
| 279. C3 | #3280 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D8 | 2 |
| #5806 | 2 |
| C2×#912 | 2 |
| #5218 | 2 |
| #5158 | 2 |
| #5157 | 2 |
| #5155 | 2 |
| #5153 | 2 |
| Dic3×D8 | 2 |
| #5116 | 2 |
| C8×#67 | 2 |
| #3280 | 3 |