Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
258 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 73 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. #5240 | C2 | semidirect |
| 3. #4545 | C2 | semidirect |
| 4. #4541 | C2 | semidirect |
| 6. C2×C3×#41 | C4 | semidirect |
| 8. C3×C4⋊Q8 | C4 | semidirect |
| 10. C3×#124 | C4 | semidirect |
| 14. C2×C3×C42 | C4 | semidirect |
| 46. C2×#41 | Dic3 | semidirect |
| 48. C4⋊Q8 | Dic3 | semidirect |
| 50. #124 | Dic3 | semidirect |
| 55. C2×C42 | Dic3 | semidirect |
| 165. C3 | #2126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#532 | 2 |
| #5240 | 2 |
| #4545 | 2 |
| #4541 | 2 |
| #2126 | 3 |