Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D3 |
| commutator | C2×C3 | C23×C4 |
| Fitting | C3×#117 | C2 |
| socle, cosocle | C22×C3 | C24 |
| prime radical | C2×#235 | C2 |
| hypercenter | #117 | D3 |
| hypocenter | C3 | #520 |
| LCS | G ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#117 | C2 | semidirect |
| 3. C2×C4⋊Dic3 | C2 | semidirect |
| 4. #892 | C2 | semidirect |
| 5. D3×C4⋊C4 | C2 | semidirect |
| 6. #67⋊C4 | C2 | semidirect |
| 7. C4×D12 | C2 | semidirect |
| 8. C4×Dic6 | C2 | semidirect |
| 13. #235 | C4 | semidirect |
| 32. #117 | D3 | semidirect |
| 37. C2×C3×C4 | C2×C4 | semidirect |
| 42. #67 | C2×C4 | semidirect |
| 46. D12 | C2×C4 | semidirect |
| 48. C4×D3 | C2×C4 | semidirect |
| 49. Dic6 | C2×C4 | semidirect |
| 90. C2×C4 | C4×D3 | semidirect |
| 113. C3 | #520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#235 | 2 |
| C3×#117 | 2 |
| C2×C4⋊Dic3 | 2 |
| #892 | 2 |
| D3×C4⋊C4 | 2 |
| #67⋊C4 | 2 |
| C4×D12 | 2 |
| C4×Dic6 | 2 |
| #520 | 3 |