Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 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 |
|---|---|---|
| 2. C2×#204 | C2 | semidirect |
| 3. #875 | C2 | semidirect |
| 4. C4×D12 | C2 | semidirect |
| 5. C3×C4⋊C8 | C2 | semidirect |
| 6. #821 | C2 | semidirect |
| 7. #816 | C2 | semidirect |
| 26. C4⋊C8 | D3 | semidirect |
| 105. C3 | #463 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D24 | 2 |
| C2×#204 | 2 |
| #875 | 2 |
| C4×D12 | 2 |
| C3×C4⋊C8 | 2 |
| #821 | 2 |
| #816 | 2 |
| #463 | 3 |