Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
480 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 145 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×#944 | C2 | semidirect |
| 5. #5225 | C2 | semidirect |
| 6. #5182 | C2 | semidirect |
| 7. #5162 | C2 | semidirect |
| 8. #5120 | C2 | semidirect |
| 9. #5118 | C2 | semidirect |
| 189. Dic3 | #137 | semidirect |
| 238. C3 | #3039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#137 | 2 |
| Dic3×#41 | 2 |
| C2×#951 | 2 |
| C2×#944 | 2 |
| #5225 | 2 |
| #5182 | 2 |
| #5162 | 2 |
| #5120 | 2 |
| #5118 | 2 |
| #3039 | 3 |