Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
152 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. #951 | C2 | semidirect |
| 3. #909 | C2 | semidirect |
| 4. #875 | C2 | semidirect |
| 5. C3×#104 | C2 | semidirect |
| 6. #823 | C2 | semidirect |
| 7. #805 | C2 | semidirect |
| 17. C2×Dic6 | C22 | semidirect |
| 18. C3×M16 | C22 | semidirect |
| 19. C3×C42 | C22 | semidirect |
| 23. #208 | C22 | semidirect |
| 31. #104 | D3 | semidirect |
| 69. M16 | C2×D3 | semidirect |
| 71. C42 | C2×D3 | semidirect |
| 123. C3 | #455 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1009 | 2 |
| #951 | 2 |
| #909 | 2 |
| #875 | 2 |
| C3×#104 | 2 |
| #823 | 2 |
| #805 | 2 |
| #455 | 3 |