Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
170 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 63 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. C2×C3×M16 | C2 | semidirect |
| 3. C2×C4×Dic3 | C2 | semidirect |
| 4. #825 | C2 | direct (N × H) |
| 11. #235 | C4 | semidirect |
| 13. C2×D12 | C4 | semidirect |
| 15. C2×Dic6 | C4 | semidirect |
| 17. C3×M16 | C22 | semidirect |
| 20. C4×Dic3 | C22 | semidirect |
| 22. C2×M16 | D3 | semidirect |
| 39. D12 | C2×C4 | semidirect |
| 43. Dic6 | C2×C4 | semidirect |
| 56. M16 | C2×D3 | semidirect |
| 94. C2×C3 | #104 | semidirect |
| 109. C3 | C2×#104 | semidirect |
| 113. C2 | #825 | 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 |
| C2×C3×M16 | 2 |
| C2×C4×Dic3 | 2 |
| #825 | 2 |
| C2×#104 | 3 |