Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
412 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 3. #5000 | C2 | direct (N × H) |
| 4. C2×C4⋊(C3⋊C8) | C2 | semidirect |
| 5. C2×#803 | C2 | semidirect |
| 6. C2×C4×C3⋊C8 | C2 | semidirect |
| 18. C4⋊(C3⋊C8) | C22 | semidirect |
| 19. #803 | C22 | semidirect |
| 20. C4×C3⋊C8 | C22 | semidirect |
| 122. C2×C3 | #433 | semidirect |
| 136. C3 | C2×#433 | semidirect |
| 138. C2 | #5000 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#117 | 2 |
| C2×#830 | 2 |
| #5000 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| C2×#803 | 2 |
| C2×C4×C3⋊C8 | 2 |
| C2×#433 | 3 |