Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×C3×#137 | C2 | semidirect |
| 3. #5816 | C2 | semidirect |
| 4. C22×#216 | C2 | semidirect |
| 5. #5233 | C2 | semidirect |
| 6. #5186 | C2 | semidirect |
| 7. #5173 | C2 | semidirect |
| 8. #5129 | C2 | semidirect |
| 9. #5120 | C2 | semidirect |
| 39. C2×#137 | D3 | semidirect |
| 275. C3 | #3011 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1010 | 2 |
| C2×C3×#137 | 2 |
| #5816 | 2 |
| C22×#216 | 2 |
| #5233 | 2 |
| #5186 | 2 |
| #5173 | 2 |
| #5129 | 2 |
| #5120 | 2 |
| #3011 | 3 |