Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
210 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 71 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×#217 | C2 | semidirect |
| 3. #834 | C2 | direct (N × H) |
| 5. C24×C3 | C4 | semidirect |
| 9. C2×C3×D4 | C4 | semidirect |
| 11. C22×C3×C4 | C4 | semidirect |
| 14. #217 | C22 | semidirect |
| 24. C23×C3 | C2×C4 | semidirect |
| 32. C2×C3×C4 | C2×C4 | semidirect |
| 35. C24 | Dic3 | semidirect |
| 39. C2×D4 | Dic3 | semidirect |
| 42. C22×C4 | Dic3 | semidirect |
| 67. C23 | C2×Dic3 | semidirect |
| 77. C2×C4 | C2×Dic3 | semidirect |
| 83. C2×C3 | #99 | semidirect |
| 101. C3 | C2×#99 | semidirect |
| 107. C2 | #834 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D4 | 2 |
| C2×#217 | 2 |
| #834 | 2 |
| C2×#99 | 3 |