Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
436 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 137 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. C3×#384 | C2 | semidirect |
| 3. C2×#809 | C2 | semidirect |
| 4. C2×C4×C3⋊C8 | C2 | semidirect |
| 13. #874 | C4 | semidirect |
| 19. #384 | D3 | semidirect |
| 37. C2×C3⋊C8 | D4 | semidirect |
| 96. C3×C4 | #102 | semidirect |
| 135. C4 | #809 | semidirect |
| 138. C3 | #1957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#874 | 2 |
| C3×#384 | 2 |
| C2×#809 | 2 |
| C2×C4×C3⋊C8 | 2 |
| #1957 | 3 |