Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
120 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 41 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. C3×C22⋊Q8 | C2 | semidirect |
| 2. C2×#215 | C2 | semidirect |
| 4. C2×#208 | C2 | semidirect |
| 5. #835 | C2 | semidirect |
| 6. #809 | C2 | semidirect |
| 7. #807 | C2 | semidirect |
| 24. C22⋊Q8 | D3 | semidirect |
| 44. C3⋊C8 | D4 | semidirect |
| 105. C3 | #468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C22⋊Q8 | 2 |
| C2×#215 | 2 |
| #930 | 2 |
| C2×#208 | 2 |
| #835 | 2 |
| #809 | 2 |
| #807 | 2 |
| #468 | 3 |