Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
418 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 207 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 |
|---|---|---|
| 3. C2×C3×C4⋊C4 | C2 | semidirect |
| 4. C2×C4⋊Dic3 | C2 | semidirect |
| 5. C2×Dic3⋊C4 | C2 | semidirect |
| 6. D3×C4⋊C4 | C2 | direct (N × H) |
| 14. C2×C4×D3 | C4 | semidirect |
| 17. C3×C4⋊C4 | C22 | semidirect |
| 18. C4⋊Dic3 | C22 | semidirect |
| 19. Dic3⋊C4 | C22 | semidirect |
| 25. C2×C4⋊C4 | D3 | direct (N × H) |
| 32. C2×C3×C4 | C2×C4 | semidirect |
| 36. C2×Dic3 | C2×C4 | semidirect |
| 40. C4×D3 | C2×C4 | semidirect |
| 52. C4⋊C4 | C2×D3 | direct (N × H) |
| 57. C2×D3 | C4⋊C4 | direct (N × H) |
| 62. C3×C4 | C22×C4 | semidirect |
| 64. Dic3 | C22×C4 | semidirect |
| 77. C2×C4 | C4×D3 | semidirect |
| 80. C2×C3 | C2×C4⋊C4 | semidirect |
| 84. D3 | C2×C4⋊C4 | direct (N × H) |
| 96. C4 | C2×C4×D3 | semidirect |
| 97. C3 | C22×C4⋊C4 | semidirect |
| 99. C2 | D3×C4⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D3 | 2 |
| C2×C3×C4⋊C4 | 2 |
| C2×C4⋊Dic3 | 2 |
| C2×Dic3⋊C4 | 2 |
| D3×C4⋊C4 | 2 |
| C22×C4⋊C4 | 3 |