Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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. C3×Q8⋊C8 | C2 | semidirect |
| 5. #4535 | C2 | semidirect |
| 6. #4484 | C2 | semidirect |
| 7. #4456 | C2 | semidirect |
| 34. Q8⋊C8 | D3 | semidirect |
| 198. C3 | #1493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5578 | 2 |
| #4837 | 2 |
| C4×D3×C8 | 2 |
| C3×Q8⋊C8 | 2 |
| #4535 | 2 |
| #4484 | 2 |
| #4456 | 2 |
| #1493 | 3 |