Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C22×C3×M16 | C2 | semidirect |
| 2. #5791 | C2 | semidirect |
| 3. C2×#904 | C2 | semidirect |
| 4. #5137 | C2 | semidirect |
| 5. #5135 | C2 | semidirect |
| 6. #5134 | C2 | semidirect |
| 7. #5113 | C2 | semidirect |
| 8. #5106 | C2 | semidirect |
| 23. C2×Dic12 | C22 | semidirect |
| 25. C2×D24 | C22 | semidirect |
| 26. C2×#204 | C22 | semidirect |
| 27. #821 | C22 | semidirect |
| 28. #818 | C22 | semidirect |
| 29. #817 | C22 | semidirect |
| 30. #816 | C22 | semidirect |
| 32. C22×M16 | D3 | semidirect |
| 56. C2×C3×C8 | D4 | semidirect |
| 136. C2×C8 | #67 | semidirect |
| 205. C3 | #3054 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×M16 | 2 |
| #5791 | 2 |
| C2×#904 | 2 |
| #5137 | 2 |
| #5135 | 2 |
| #5134 | 2 |
| #5113 | 2 |
| #5106 | 2 |
| #3054 | 3 |