Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
322 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
| 5. C2×C4⋊Dic3 | C2 | semidirect |
| 6. #897 | C2 | direct (N × H) |
| 16. C2×Dic6 | C22 | semidirect |
| 17. C3×C4⋊C4 | C22 | semidirect |
| 19. C4⋊Dic3 | C22 | semidirect |
| 24. C2×C4⋊C4 | D3 | semidirect |
| 29. C22×D3 | Q8 | semidirect |
| 51. C4⋊C4 | C2×D3 | semidirect |
| 60. C2×D3 | C2×Q8 | semidirect |
| 80. C2×C3 | C22⋊Q8 | semidirect |
| 97. C3 | C2×C22⋊Q8 | semidirect |
| 99. C2 | #897 | 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×C4⋊Dic3 | 2 |
| #897 | 2 |
| C2×C22⋊Q8 | 3 |