Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
184 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 184 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 |
|---|---|---|
| 3. C3×C4⋊C16 | C2 | semidirect |
| 4. Dic3⋊C16 | C2 | semidirect |
| 5. C4⋊(C3⋊C16) | C2 | semidirect |
| 21. C4⋊C16 | D3 | direct (N × H) |
| 56. C4×D3 | C16 | semidirect |
| 85. C3×C4 | C2×C16 | semidirect |
| 90. Dic3 | C2×C16 | semidirect |
| 110. D3 | C4⋊C16 | direct (N × H) |
| 119. C4 | D3×C16 | semidirect |
| 122. C3 | C2×C4⋊C16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×C16 | 2 |
| C4×D3×C8 | 2 |
| C3×C4⋊C16 | 2 |
| Dic3⋊C16 | 2 |
| C4⋊(C3⋊C16) | 2 |
| C2×C4⋊C16 | 3 |