Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
236 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 99 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 | #555 |
| 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. #938 | C2 | semidirect |
| 3. #930 | C2 | semidirect |
| 4. #926 | C2 | semidirect |
| 5. #892 | C2 | semidirect |
| 6. #885 | C2 | semidirect |
| 7. C4×D12 | C2 | semidirect |
| 8. #869 | C2 | semidirect |
| 31. C4×D4 | D3 | semidirect |
| 109. C3 | #555 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D4 | 2 |
| #938 | 2 |
| #930 | 2 |
| #926 | 2 |
| #892 | 2 |
| #885 | 2 |
| C4×D12 | 2 |
| #869 | 2 |
| #555 | 3 |