Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
216 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 73 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×C4×M16 | C2 | semidirect |
| 4. #5124 | C2 | semidirect |
| 6. #4559 | C2 | semidirect |
| 7. #4523 | C2 | semidirect |
| 19. #824 | C4 | semidirect |
| 20. #823 | C4 | semidirect |
| 28. C4×M16 | D3 | semidirect |
| 185. C3 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×M16 | 2 |
| #5139 | 2 |
| #5132 | 2 |
| #5124 | 2 |
| C2×#805 | 2 |
| #4559 | 2 |
| #4523 | 2 |
| #1932 | 3 |