Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
330 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 159 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. C3×#117 | C2 | semidirect |
| 3. #926 | C2 | semidirect |
| 4. #892 | C2 | semidirect |
| 5. D3×C4⋊C4 | C2 | semidirect |
| 7. #877 | C2 | semidirect |
| 8. #872 | C2 | semidirect |
| 9. C42×D3 | C2 | semidirect |
| 14. C2×C4×D3 | C4 | semidirect |
| 20. C3×C4⋊C4 | C22 | semidirect |
| 22. C3×C42 | C22 | semidirect |
| 25. C4⋊Dic3 | C22 | semidirect |
| 26. Dic3⋊C4 | C22 | semidirect |
| 27. C4×Dic3 | C22 | semidirect |
| 28. C4×Dic3 | C22 | semidirect |
| 34. #117 | D3 | direct (N × H) |
| 43. C2×C3×C4 | C2×C4 | semidirect |
| 47. C2×Dic3 | C2×C4 | semidirect |
| 54. C4×D3 | C2×C4 | semidirect |
| 55. C4×D3 | C2×C4 | semidirect |
| 67. C4⋊C4 | C2×D3 | semidirect |
| 73. C42 | C2×D3 | semidirect |
| 102. C2×C4 | C4×D3 | semidirect |
| 110. D3 | #117 | direct (N × H) |
| 125. C3 | C2×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D3 | 2 |
| C3×#117 | 2 |
| #926 | 2 |
| #892 | 2 |
| D3×C4⋊C4 | 2 |
| D3×C22⋊C4 | 2 |
| #877 | 2 |
| #872 | 2 |
| C42×D3 | 2 |
| C2×#117 | 3 |