Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
154 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 59 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. #926 | C2 | semidirect |
| 4. #825 | C2 | semidirect |
| 10. #235 | C4 | semidirect |
| 12. C2×D12 | C4 | semidirect |
| 14. C2×Dic6 | C4 | semidirect |
| 16. C3×M16 | C22 | semidirect |
| 20. C4×Dic3 | C22 | semidirect |
| 22. C2×M16 | D3 | semidirect |
| 54. M16 | C2×D3 | semidirect |
| 107. C3 | #421 | 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 |
| #926 | 2 |
| #825 | 2 |
| #421 | 3 |