Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 3. C4×Dic6 | C2 | semidirect |
| 4. C3×#97 | C2 | semidirect |
| 6. #818 | C2 | semidirect |
| 7. #816 | C2 | semidirect |
| 20. #204 | C4 | semidirect |
| 27. #97 | D3 | semidirect |
| 39. Dic6 | C2×C4 | semidirect |
| 41. C3×C8 | C2×C4 | semidirect |
| 78. C8 | C4×D3 | semidirect |
| 94. C3 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#204 | 2 |
| C4×D12 | 2 |
| C4×Dic6 | 2 |
| C3×#97 | 2 |
| #821 | 2 |
| #818 | 2 |
| #816 | 2 |
| #440 | 3 |