Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
300 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 125 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. #5101 | C2 | semidirect |
| 5. C2×C8×Dic3 | C2 | semidirect |
| 6. #4558 | C2 | semidirect |
| 7. #4555 | C2 | semidirect |
| 11. C3×#131 | C4 | semidirect |
| 20. #837 | C4 | semidirect |
| 21. #835 | C4 | semidirect |
| 22. #832 | C4 | semidirect |
| 65. #131 | Dic3 | semidirect |
| 191. C3 | #1764 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#131 | 2 |
| C2×#837 | 2 |
| #5233 | 2 |
| #5101 | 2 |
| C2×C8×Dic3 | 2 |
| #4558 | 2 |
| #4555 | 2 |
| #1764 | 3 |