Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
108 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 37 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. C3×AGL(1,ℤ/8) | C2 | semidirect |
| 2. #949 | C2 | semidirect |
| 3. #948 | C2 | semidirect |
| 4. C2×#213 | C2 | semidirect |
| 5. #833 | C2 | semidirect |
| 6. #823 | C2 | semidirect |
| 7. #822 | C2 | semidirect |
| 25. AGL(1,ℤ/8) | D3 | semidirect |
| 101. C3 | #472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×AGL(1,ℤ/8) | 2 |
| #949 | 2 |
| #948 | 2 |
| C2×#213 | 2 |
| #833 | 2 |
| #823 | 2 |
| #822 | 2 |
| #472 | 3 |