Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. C3×#536 | C2 | semidirect |
| 3. C2×#948 | C2 | semidirect |
| 4. C22×#215 | C2 | semidirect |
| 5. #5225 | C2 | semidirect |
| 6. #5049 | C2 | semidirect |
| 7. #5048 | C2 | semidirect |
| 8. #5001 | C2 | semidirect |
| 9. #4998 | C2 | semidirect |
| 17. C3×C22⋊Q8 | C22 | semidirect |
| 29. C2×#208 | C22 | semidirect |
| 31. C22×C3⋊C8 | C22 | semidirect |
| 32. #835 | C22 | semidirect |
| 34. #808 | C22 | semidirect |
| 35. #807 | C22 | semidirect |
| 38. #536 | D3 | semidirect |
| 77. C2×C3⋊C8 | D4 | semidirect |
| 97. C22⋊Q8 | C2×D3 | semidirect |
| 235. C3 | #3057 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#536 | 2 |
| #5830 | 2 |
| C2×#948 | 2 |
| C22×#215 | 2 |
| #5225 | 2 |
| #5049 | 2 |
| #5048 | 2 |
| #5001 | 2 |
| #4998 | 2 |
| #3057 | 3 |