Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
162 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 162 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. #821 | C2 | semidirect |
| 5. #816 | C2 | semidirect |
| 11. #235 | C4 | semidirect |
| 20. C2×M16 | D3 | semidirect |
| 35. D12 | C2×C4 | semidirect |
| 38. Dic6 | C2×C4 | semidirect |
| 97. C3 | #417 | semidirect |
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 |
| #821 | 2 |
| #816 | 2 |
| #417 | 3 |