Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 1. #1010 | C2 | semidirect |
| 2. C3×AGL(1,ℤ/8) | C2 | semidirect |
| 3. #936 | C2 | semidirect |
| 4. #932 | C2 | semidirect |
| 5. #837 | C2 | semidirect |
| 6. #825 | C2 | semidirect |
| 7. #824 | C2 | semidirect |
| 28. AGL(1,ℤ/8) | D3 | semidirect |
| 121. C3 | #454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1010 | 2 |
| C3×AGL(1,ℤ/8) | 2 |
| #936 | 2 |
| #932 | 2 |
| #837 | 2 |
| #825 | 2 |
| #824 | 2 |
| #454 | 3 |