Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
124 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 124 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×SD16 | C2 | semidirect |
| 2. #946 | C2 | semidirect |
| 4. C2×D3×C8 | C2 | semidirect |
| 5. #835 | C2 | semidirect |
| 6. #832 | C2 | semidirect |
| 7. #817 | C2 | semidirect |
| 22. C2×SD16 | D3 | semidirect |
| 43. C3×C8 | D4 | semidirect |
| 64. C2×D3 | SD16 | semidirect |
| 86. C8 | #67 | semidirect |
| 105. C3 | #465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×SD16 | 2 |
| #946 | 2 |
| #938 | 2 |
| C2×D3×C8 | 2 |
| #835 | 2 |
| #832 | 2 |
| #817 | 2 |
| #465 | 3 |