Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
158 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 1. C2×D3×Q8 | C2 | semidirect |
| 2. C2×#215 | C2 | semidirect |
| 3. C2×#204 | C2 | semidirect |
| 5. C3×#103 | C2 | semidirect |
| 6. (C2×D3)⋊C8 | C2 | semidirect |
| 7. #810 | C2 | semidirect |
| 29. #103 | D3 | semidirect |
| 34. C3×Q8 | D4 | semidirect |
| 48. Dic6 | D4 | semidirect |
| 72. C2×D3 | SD16 | semidirect |
| 85. Q8 | D12 | semidirect |
| 117. C3 | #448 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×Q8 | 2 |
| C2×#215 | 2 |
| C2×#204 | 2 |
| #895 | 2 |
| C3×#103 | 2 |
| (C2×D3)⋊C8 | 2 |
| #810 | 2 |
| #448 | 3 |