Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
446 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 137 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×#909 | C2 | semidirect |
| 3. C2×#909 | C2 | semidirect |
| 4. #5745 | C2 | semidirect |
| 5. C3×#430 | C2 | semidirect |
| 6. C2×#824 | C2 | semidirect |
| 7. #5132 | C2 | semidirect |
| 8. #4898 | C2 | semidirect |
| 9. #4896 | C2 | semidirect |
| 29. C2×Dic12 | C22 | semidirect |
| 32. C2×#204 | C22 | semidirect |
| 34. C3×#108 | C22 | semidirect |
| 35. #824 | C22 | semidirect |
| 36. #824 | C22 | semidirect |
| 37. #823 | C22 | semidirect |
| 44. #430 | D3 | semidirect |
| 116. #108 | C2×D3 | semidirect |
| 278. C3 | #3069 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5748 | 2 |
| C2×#909 | 2 |
| #5745 | 2 |
| C3×#430 | 2 |
| C2×#824 | 2 |
| #5132 | 2 |
| #4898 | 2 |
| #4896 | 2 |
| #3069 | 3 |