Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
138 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 67 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 |
|---|---|---|
| 2. C3×C4⋊C16 | C2 | semidirect |
| 5. #4502 | C2 | semidirect |
| 6. Dic3×C16 | C2 | semidirect |
| 7. C4⋊(C3⋊C16) | C2 | semidirect |
| 22. C4⋊C16 | D3 | semidirect |
| 128. C3 | #2164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #4689 | 2 |
| C3×C4⋊C16 | 2 |
| (C2×D3)⋊C16 | 2 |
| #4502 | 2 |
| Dic3×C16 | 2 |
| C4⋊(C3⋊C16) | 2 |
| #2164 | 3 |