Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 10. C2×C3×C16 | C4 | semidirect |
| 15. C2×C3⋊C16 | C4 | semidirect |
| 42. C2×C16 | Dic3 | semidirect |
| 54. C2×Dic3 | C16 | semidirect |
| 115. C3 | #1374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C16 | 2 |
| C2×C8×Dic3 | 2 |
| C22×C3⋊C16 | 2 |
| #1374 | 3 |