Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 149 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. C3×#536 | C2 | semidirect |
| 3. C2×#942 | C2 | semidirect |
| 4. C22×#215 | C2 | semidirect |
| 5. #5234 | C2 | semidirect |
| 6. #5047 | C2 | semidirect |
| 7. #5046 | C2 | semidirect |
| 8. #5002 | C2 | semidirect |
| 9. #5001 | C2 | semidirect |
| 12. C22×C3×Q8 | C22 | semidirect |
| 25. C3×C22⋊Q8 | C22 | semidirect |
| 26. C3×#117 | C22 | semidirect |
| 27. C2×#216 | C22 | semidirect |
| 30. C2×#215 | C22 | semidirect |
| 31. C2×#215 | C22 | semidirect |
| 32. C2×#208 | C22 | semidirect |
| 33. C22×C3⋊C8 | C22 | semidirect |
| 34. #830 | C22 | semidirect |
| 35. #810 | C22 | semidirect |
| 36. #809 | C22 | semidirect |
| 37. #809 | C22 | semidirect |
| 41. #536 | D3 | semidirect |
| 99. C22×Q8 | C2×D3 | semidirect |
| 114. C22⋊Q8 | C2×D3 | semidirect |
| 115. #117 | C2×D3 | semidirect |
| 286. C3 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1009 | 2 |
| C3×#536 | 2 |
| C2×#942 | 2 |
| C22×#215 | 2 |
| #5234 | 2 |
| #5047 | 2 |
| #5046 | 2 |
| #5002 | 2 |
| #5001 | 2 |
| #3009 | 3 |