Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
148 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 148 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. C3×#504 | C2 | semidirect |
| 2. #5142 | C2 | semidirect |
| 3. C2×D48 | C2 | semidirect |
| 4. #4516 | C2 | semidirect |
| 5. #4506 | C2 | semidirect |
| 19. #504 | D3 | semidirect |
| 104. C3 | #2221 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#504 | 2 |
| #5142 | 2 |
| C2×D48 | 2 |
| #4516 | 2 |
| #4506 | 2 |
| #2221 | 3 |