Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
120 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 43 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×C3×M16 | C2 | semidirect |
| 3. #924 | C2 | semidirect |
| 4. C2×#204 | C2 | semidirect |
| 5. #821 | C2 | semidirect |
| 6. #818 | C2 | semidirect |
| 7. #816 | C2 | semidirect |
| 23. C2×M16 | D3 | semidirect |
| 44. C3×C8 | D4 | semidirect |
| 86. C8 | #67 | semidirect |
| 105. C3 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×M16 | 2 |
| #930 | 2 |
| #924 | 2 |
| C2×#204 | 2 |
| #821 | 2 |
| #818 | 2 |
| #816 | 2 |
| #468 | 3 |