Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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×C3×SD32 | C2 | semidirect |
| 2. #5188 | C2 | semidirect |
| 4. C2×#798 | C2 | semidirect |
| 5. #4564 | C2 | semidirect |
| 6. #4562 | C2 | semidirect |
| 7. #4504 | C2 | semidirect |
| 22. C2×SD32 | D3 | semidirect |
| 46. C3×C16 | D4 | semidirect |
| 96. C16 | #67 | semidirect |
| 145. C3 | #2220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×SD32 | 2 |
| #5188 | 2 |
| #5157 | 2 |
| C2×#798 | 2 |
| #4564 | 2 |
| #4562 | 2 |
| #4504 | 2 |
| #2220 | 3 |