Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 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 |
|---|---|---|
| 2. C3×C22⋊Q8 | C2 | semidirect |
| 3. C2×#216 | C2 | semidirect |
| 4. C2×#215 | C2 | semidirect |
| 5. #830 | C2 | semidirect |
| 6. #810 | C2 | semidirect |
| 7. #809 | C2 | semidirect |
| 27. C22⋊Q8 | D3 | semidirect |
| 115. C3 | #452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#235 | 2 |
| C3×C22⋊Q8 | 2 |
| C2×#216 | 2 |
| C2×#215 | 2 |
| #830 | 2 |
| #810 | 2 |
| #809 | 2 |
| #452 | 3 |