Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 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×SD16 | C2 | semidirect |
| 3. #946 | C2 | semidirect |
| 4. C2×#215 | C2 | semidirect |
| 5. #832 | C2 | semidirect |
| 6. #821 | C2 | semidirect |
| 7. (C2×D3)⋊C8 | C2 | semidirect |
| 10. C2×C3×Q8 | C22 | semidirect |
| 18. C2×C3×C8 | C22 | semidirect |
| 21. C4⋊Dic3 | C22 | semidirect |
| 23. C2×C3⋊C8 | C22 | semidirect |
| 26. C2×SD16 | D3 | semidirect |
| 53. C2×Q8 | C2×D3 | semidirect |
| 63. C2×C8 | C2×D3 | semidirect |
| 77. C2×D3 | SD16 | semidirect |
| 126. C3 | #450 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D4 | 2 |
| C2×C3×SD16 | 2 |
| #946 | 2 |
| C2×#215 | 2 |
| #832 | 2 |
| #821 | 2 |
| (C2×D3)⋊C8 | 2 |
| #450 | 3 |