Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
212 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 53 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. #5020 | C2 | semidirect |
| 3. #4849 | C2 | semidirect |
| 5. C3×Q8⋊C8 | C2 | semidirect |
| 7. #4456 | C2 | semidirect |
| 32. Q8⋊C8 | D3 | semidirect |
| 176. C3 | #1640 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5585 | 2 |
| #5020 | 2 |
| #4849 | 2 |
| #4694 | 2 |
| C3×Q8⋊C8 | 2 |
| #4485 | 2 |
| #4456 | 2 |
| #1640 | 3 |