Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 95 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, socle, cosocle | C22×C3 | C24 |
| Fitting | C3×C4×D4 | C2 |
| hypercenter | C4×D4 | D3 |
| hypocenter | C3 | #540 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C4×D4 | C2 | semidirect |
| 2. #940 | C2 | semidirect |
| 3. #938 | C2 | semidirect |
| 4. #930 | C2 | semidirect |
| 5. #929 | C2 | semidirect |
| 6. #895 | C2 | semidirect |
| 7. #890 | C2 | semidirect |
| 8. #884 | C2 | semidirect |
| 9. #883 | C2 | semidirect |
| 10. C4×D12 | C2 | semidirect |
| 11. #872 | C2 | semidirect |
| 45. C4×D4 | D3 | semidirect |
| 152. C3 | #540 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D4 | 2 |
| #940 | 2 |
| #938 | 2 |
| #930 | 2 |
| #929 | 2 |
| #895 | 2 |
| #890 | 2 |
| #884 | 2 |
| #883 | 2 |
| C4×D12 | 2 |
| #872 | 2 |
| #540 | 3 |