Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
548 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 97 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. C3×#410 | C2 | semidirect |
| 3. #5234 | C2 | semidirect |
| 4. #5005 | C2 | semidirect |
| 5. #5002 | C2 | semidirect |
| 11. #1007 | C4 | semidirect |
| 13. #1004 | C4 | semidirect |
| 16. C3×#117 | C22 | semidirect |
| 17. C2×#208 | C22 | semidirect |
| 18. C22×C3⋊C8 | C22 | semidirect |
| 27. #410 | D3 | semidirect |
| 75. #117 | C2×D3 | semidirect |
| 211. C3 | #1794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5964 | 2 |
| C3×#410 | 2 |
| #5234 | 2 |
| #5005 | 2 |
| #5002 | 2 |
| #1794 | 3 |