Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
186 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 63 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×C3×M16 | C2 | semidirect |
| 3. C2×#208 | C2 | semidirect |
| 4. #823 | C2 | direct (N × H) |
| 15. C3×M16 | C22 | semidirect |
| 18. #208 | C22 | semidirect |
| 22. C2×M16 | D3 | semidirect |
| 52. M16 | C2×D3 | semidirect |
| 86. C2×C3 | #100 | semidirect |
| 101. C3 | C2×#100 | semidirect |
| 105. C2 | #823 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D12 | 2 |
| C2×C3×M16 | 2 |
| C2×#208 | 2 |
| #823 | 2 |
| C2×#100 | 3 |