Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
330 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 167 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×C4⋊C4 | C2 | semidirect |
| 4. C2×C4⋊Dic3 | C2 | semidirect |
| 5. C2×C4×Dic3 | C2 | semidirect |
| 6. #892 | C2 | direct (N × H) |
| 13. C2×C4×D3 | C4 | semidirect |
| 15. C3×C4⋊C4 | C22 | semidirect |
| 17. C4⋊Dic3 | C22 | semidirect |
| 18. C4×Dic3 | C22 | semidirect |
| 22. C2×C4⋊C4 | D3 | semidirect |
| 38. C4×D3 | C2×C4 | semidirect |
| 47. C4⋊C4 | C2×D3 | semidirect |
| 76. C2×C3 | #117 | semidirect |
| 93. C3 | C2×#117 | semidirect |
| 95. C2 | #892 | 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×(C2×D3)⋊C4 | 2 |
| C2×C4⋊Dic3 | 2 |
| C2×C4×Dic3 | 2 |
| #892 | 2 |
| C2×#117 | 3 |