Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 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. D3×M16 | C2 | semidirect |
| 3. C3×#100 | C2 | semidirect |
| 4. #833 | C2 | semidirect |
| 5. #823 | C2 | semidirect |
| 14. C3×M16 | C22 | semidirect |
| 15. #208 | C22 | semidirect |
| 22. #100 | D3 | direct (N × H) |
| 47. M16 | C2×D3 | semidirect |
| 81. D3 | #100 | direct (N × H) |
| 94. C3 | C2×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D4 | 2 |
| D3×M16 | 2 |
| C3×#100 | 2 |
| #833 | 2 |
| #823 | 2 |
| C2×#100 | 3 |