Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
292 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×#815 | C2 | semidirect |
| 5. #4997 | C2 | semidirect |
| 6. #4552 | C2 | semidirect |
| 7. #4532 | C2 | semidirect |
| 13. #948 | C4 | semidirect |
| 20. C3×#103 | C4 | semidirect |
| 21. C3×#102 | C4 | semidirect |
| 22. #837 | C4 | semidirect |
| 75. #103 | Dic3 | semidirect |
| 76. #102 | Dic3 | semidirect |
| 191. C3 | #1765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#948 | 2 |
| C3×#416 | 2 |
| C2×#837 | 2 |
| C2×#815 | 2 |
| #4997 | 2 |
| #4552 | 2 |
| #4532 | 2 |
| #1765 | 3 |