Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
162 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 47 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. C2×C3×#41 | C2 | semidirect |
| 2. C2×#215 | C2 | semidirect |
| 3. C2×#213 | C2 | semidirect |
| 4. #930 | C2 | semidirect |
| 5. #835 | C2 | semidirect |
| 6. #832 | C2 | semidirect |
| 7. #830 | C2 | semidirect |
| 24. C2×#41 | D3 | semidirect |
| 35. C3×Q8 | D4 | semidirect |
| 38. C3×D4 | D4 | semidirect |
| 85. Q8 | #67 | semidirect |
| 91. D4 | #67 | semidirect |
| 122. C3 | #449 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41 | 2 |
| C2×#215 | 2 |
| C2×#213 | 2 |
| #930 | 2 |
| #835 | 2 |
| #832 | 2 |
| #830 | 2 |
| #449 | 3 |