Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
134 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 134 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 |
|---|---|---|
| 1. C22×C3×C8 | C2 | semidirect |
| 3. C2×D3×C8 | C2 | semidirect |
| 4. #830 | C2 | semidirect |
| 5. (C2×D3)⋊C8 | C2 | semidirect |
| 6. Dic3⋊C8 | C2 | semidirect |
| 7. C8×Dic3 | C2 | semidirect |
| 23. C22×C8 | D3 | semidirect |
| 35. #67 | C8 | direct (N × H) |
| 42. C3×C8 | D4 | semidirect |
| 60. C22×C3 | C2×C8 | semidirect |
| 64. C2×D3 | C2×C8 | semidirect |
| 70. Dic3 | C2×C8 | semidirect |
| 86. C8 | #67 | direct (N × H) |
| 97. C22 | D3×C8 | semidirect |
| 105. C3 | C8×D4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C8 | 2 |
| C4×#67 | 2 |
| C2×D3×C8 | 2 |
| #830 | 2 |
| (C2×D3)⋊C8 | 2 |
| Dic3⋊C8 | 2 |
| C8×Dic3 | 2 |
| C8×D4 | 3 |