Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
572 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#909 | C2 | semidirect |
| 2. C2×#908 | C2 | semidirect |
| 3. #5477 | C2 | semidirect |
| 4. C2×#875 | C2 | semidirect |
| 5. C3×C4×M16 | C2 | semidirect |
| 6. #4715 | C2 | semidirect |
| 7. #4712 | C2 | semidirect |
| 8. #4696 | C2 | semidirect |
| 19. C2×Dic12 | C22 | semidirect |
| 22. C2×#204 | C22 | semidirect |
| 26. #875 | C22 | semidirect |
| 27. #874 | C22 | semidirect |
| 29. #869 | C22 | semidirect |
| 30. C3×#97 | C22 | semidirect |
| 31. C3×C4×C8 | C22 | semidirect |
| 39. C4×M16 | D3 | semidirect |
| 57. C3×M16 | D4 | semidirect |
| 90. #97 | C2×D3 | semidirect |
| 91. C4×C8 | C2×D3 | semidirect |
| 139. M16 | D12 | semidirect |
| 207. C3 | #3153 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#909 | 2 |
| C2×#908 | 2 |
| #5477 | 2 |
| C2×#875 | 2 |
| C3×C4×M16 | 2 |
| #4715 | 2 |
| #4712 | 2 |
| #4696 | 2 |
| #3153 | 3 |