Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
286 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 77 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. C22×C4×D3 | C2 | semidirect |
| 3. C2×C3×C22⋊C4 | C2 | semidirect |
| 4. C2×#217 | C2 | semidirect |
| 5. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C3⋊#95 | C2 | semidirect |
| 7. C3⋊#95 | C2 | semidirect |
| 15. C2×#67 | C4 | semidirect |
| 29. C2×C22⋊C4 | D3 | semidirect |
| 38. C23×C3 | C2×C4 | semidirect |
| 52. C2×C3×C4 | D4 | semidirect |
| 61. C2×Dic3 | C2×C4 | semidirect |
| 62. C2×Dic3 | D4 | semidirect |
| 100. C2×D3 | C22⋊C4 | semidirect |
| 119. C23 | C4×D3 | semidirect |
| 137. C2×C4 | #67 | semidirect |
| 173. C3 | #386 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67 | 2 |
| C22×C4×D3 | 2 |
| C2×C3×C22⋊C4 | 2 |
| C2×#217 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| C3⋊#95 | 2 |
| #386 | 3 |