Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
160 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 79 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. C3×C4⋊C16 | C2 | semidirect |
| 5. Dic3⋊C16 | C2 | semidirect |
| 6. Dic3⋊C16 | C2 | semidirect |
| 7. C4⋊(C3⋊C16) | C2 | semidirect |
| 28. C4⋊C16 | D3 | semidirect |
| 132. C3 | #2151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#798 | 2 |
| C2×D3×C16 | 2 |
| #4689 | 2 |
| C3×C4⋊C16 | 2 |
| Dic3⋊C16 | 2 |
| C4⋊(C3⋊C16) | 2 |
| #2151 | 3 |