Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
322 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
| 4. C2×C4⋊Dic3 | C2 | semidirect |
| 5. #924 | C2 | direct (N × H) |
| 6. C2×Dic3⋊C4 | C2 | semidirect |
| 16. C2×Dic6 | C22 | semidirect |
| 18. C4⋊Dic3 | C22 | semidirect |
| 19. Dic3⋊C4 | C22 | semidirect |
| 28. C23×C3 | Q8 | semidirect |
| 58. C22×C3 | C2×Q8 | semidirect |
| 67. C23 | Dic6 | semidirect |
| 81. C2×C3 | C22⋊Q8 | semidirect |
| 89. C22 | C2×Dic6 | semidirect |
| 97. C3 | C2×C22⋊Q8 | semidirect |
| 99. C2 | #924 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4 | 2 |
| C22×Dic6 | 2 |
| C2×#217 | 2 |
| C2×C4⋊Dic3 | 2 |
| #924 | 2 |
| C2×Dic3⋊C4 | 2 |
| C2×C22⋊Q8 | 3 |