Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
144 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. C3×#504 | C2 | semidirect |
| 2. #5143 | C2 | semidirect |
| 4. C2×#800 | C2 | semidirect |
| 5. #4517 | C2 | semidirect |
| 6. #4516 | C2 | semidirect |
| 7. #4506 | C2 | semidirect |
| 25. #504 | D3 | semidirect |
| 138. C3 | #2223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#504 | 2 |
| #5143 | 2 |
| #5142 | 2 |
| C2×#800 | 2 |
| #4517 | 2 |
| #4516 | 2 |
| #4506 | 2 |
| #2223 | 3 |