Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
180 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 4. #4458 | C2 | semidirect |
| 5. #4457 | C2 | semidirect |
| 28. C3×M16 | C8 | semidirect |
| 64. C3×C8 | C2×C8 | semidirect |
| 72. M16 | C3⋊C8 | semidirect |
| 111. C8 | C2×C3⋊C8 | semidirect |
| 128. C3 | #1565 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×M16 | 2 |
| #4925 | 2 |
| C2×C4⋊(C3⋊C8) | 2 |
| #4458 | 2 |
| #4457 | 2 |
| #1565 | 3 |