Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
338 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 151 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×C22⋊C4 | C2 | semidirect |
| 3. C2×#217 | C2 | semidirect |
| 4. C4×#67 | C2 | semidirect |
| 5. #67⋊C4 | C2 | semidirect |
| 6. D3×C22⋊C4 | C2 | semidirect |
| 7. #877 | C2 | semidirect |
| 11. C22×C3×C4 | C22 | semidirect |
| 12. C2×#67 | C4 | semidirect |
| 16. C22×Dic3 | C22 | semidirect |
| 17. C2×C4×D3 | C22 | semidirect |
| 19. C3×C22⋊C4 | C22 | semidirect |
| 21. #217 | C22 | semidirect |
| 22. (C2×D3)⋊C4 | C22 | semidirect |
| 23. Dic3⋊C4 | C22 | semidirect |
| 24. C4×Dic3 | C22 | semidirect |
| 31. C2×C22⋊C4 | D3 | semidirect |
| 33. C23×C3 | C2×C4 | semidirect |
| 38. C22×D3 | C2×C4 | semidirect |
| 42. #67 | C2×C4 | semidirect |
| 43. #67 | C2×C4 | semidirect |
| 45. C2×Dic3 | C2×C4 | semidirect |
| 57. C22×C4 | C2×D3 | semidirect |
| 63. C22⋊C4 | C2×D3 | semidirect |
| 83. C23 | C4×D3 | semidirect |
| 116. C3 | #518 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67 | 2 |
| C2×C3×C22⋊C4 | 2 |
| C2×#217 | 2 |
| C4×#67 | 2 |
| #67⋊C4 | 2 |
| D3×C22⋊C4 | 2 |
| #877 | 2 |
| #518 | 3 |