Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
266 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 65 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×#413 | C2 | semidirect |
| 3. #5240 | C2 | semidirect |
| 4. #4475 | C2 | semidirect |
| 7. C22×D12 | C4 | semidirect |
| 11. #937 | C4 | semidirect |
| 16. #926 | C4 | semidirect |
| 22. #413 | D3 | semidirect |
| 192. C3 | #2122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #5830 | 2 |
| C3×#413 | 2 |
| #5240 | 2 |
| #4475 | 2 |
| #2122 | 3 |