Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
278 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. C2×#822 | C2 | semidirect |
| 5. C2×#819 | C2 | semidirect |
| 6. C3×#341 | C2 | semidirect |
| 7. #4558 | C2 | semidirect |
| 32. #341 | D3 | semidirect |
| 155. C2×D3 | #108 | semidirect |
| 219. C3 | #1855 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×M16 | 2 |
| #5126 | 2 |
| C2×#822 | 2 |
| C2×(C2×D3)⋊C8 | 2 |
| C2×#819 | 2 |
| C3×#341 | 2 |
| #4558 | 2 |
| #1855 | 3 |