Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
184 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 109 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×#346 | C2 | semidirect |
| 5. #4502 | C2 | semidirect |
| 6. Dic3×C16 | C2 | semidirect |
| 7. C4×C3⋊C16 | C2 | semidirect |
| 20. #798 | C4 | semidirect |
| 21. D3×C16 | C4 | semidirect |
| 26. #346 | D3 | semidirect |
| 117. C3 | #2108 | 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×#346 | 2 |
| #4502 | 2 |
| Dic3×C16 | 2 |
| C4×C3⋊C16 | 2 |
| #2108 | 3 |