Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
322 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 127 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. C22×Dic6 | C2 | semidirect |
| 3. C2×C3×C4⋊C4 | C2 | semidirect |
| 6. C2×Dic3⋊C4 | C2 | semidirect |
| 7. C2×Dic3⋊C4 | C2 | semidirect |
| 8. #896 | C2 | direct (N × H) |
| 20. C2×Dic6 | C22 | semidirect |
| 21. C3×C4⋊C4 | C22 | semidirect |
| 24. Dic3⋊C4 | C22 | semidirect |
| 25. Dic3⋊C4 | C22 | semidirect |
| 31. C2×C4⋊C4 | D3 | semidirect |
| 37. C22×D3 | Q8 | semidirect |
| 66. C4⋊C4 | C2×D3 | semidirect |
| 76. C2×D3 | C2×Q8 | semidirect |
| 102. C2×C3 | C22⋊Q8 | semidirect |
| 121. C3 | C2×C22⋊Q8 | semidirect |
| 123. C2 | #896 | 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 |
| C22×Dic6 | 2 |
| C2×C3×C4⋊C4 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| C2×Dic3⋊C4 | 2 |
| #896 | 2 |
| C2×C22⋊Q8 | 3 |