Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #5470 | C2 | semidirect |
| 3. C3×C4×M16 | C2 | semidirect |
| 5. #5120 | C2 | semidirect |
| 6. #4714 | C2 | semidirect |
| 7. #4697 | C2 | semidirect |
| 19. #870 | C22 | semidirect |
| 20. #869 | C22 | semidirect |
| 22. C3×#97 | C22 | semidirect |
| 23. C3×C4×C8 | C22 | semidirect |
| 25. #816 | C22 | semidirect |
| 32. C4×M16 | D3 | semidirect |
| 71. #97 | C2×D3 | semidirect |
| 72. C4×C8 | C2×D3 | semidirect |
| 162. C3 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#875 | 2 |
| #5470 | 2 |
| C3×C4×M16 | 2 |
| #5131 | 2 |
| #5120 | 2 |
| #4714 | 2 |
| #4697 | 2 |
| #3140 | 3 |