Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
258 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 111 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. C22×Dic6 | C2 | semidirect |
| 3. C2×C3×M16 | C2 | semidirect |
| 4. #909 | C2 | direct (N × H) |
| 5. C2×Dic12 | C2 | semidirect |
| 6. C2×#204 | C2 | semidirect |
| 19. C2×Dic6 | C22 | semidirect |
| 20. C3×M16 | C22 | semidirect |
| 22. Dic12 | C22 | semidirect |
| 23. #204 | C22 | semidirect |
| 29. C2×M16 | D3 | semidirect |
| 63. M16 | C2×D3 | semidirect |
| 95. C2×C3 | #137 | semidirect |
| 108. C3 | C2×#137 | semidirect |
| 111. C2 | #909 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#235 | 2 |
| C22×Dic6 | 2 |
| C2×C3×M16 | 2 |
| #909 | 2 |
| C2×Dic12 | 2 |
| C2×#204 | 2 |
| C2×#137 | 3 |