Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
142 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 142 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×SD16 | C2 | semidirect |
| 2. #944 | C2 | semidirect |
| 3. C2×#215 | C2 | semidirect |
| 5. C2×#214 | C2 | semidirect |
| 6. C2×#204 | C2 | semidirect |
| 7. C8×Dic3 | C2 | semidirect |
| 25. C2×SD16 | D3 | semidirect |
| 44. C3×C8 | D4 | semidirect |
| 45. C3⋊C8 | D4 | semidirect |
| 68. Dic3 | SD16 | semidirect |
| 85. C8 | #67 | semidirect |
| 100. C3 | #492 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×SD16 | 2 |
| #944 | 2 |
| C2×#215 | 2 |
| #940 | 2 |
| C2×#214 | 2 |
| C2×#204 | 2 |
| C8×Dic3 | 2 |
| #492 | 3 |