Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 23. C3×Q16 | C8 | semidirect |
| 56. Q16 | C3⋊C8 | semidirect |
| 95. C3 | #1579 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Q16 | 2 |
| Q8×C3⋊C8 | 2 |
| #4535 | 2 |
| #4457 | 2 |
| #4455 | 2 |
| #1579 | 3 |