Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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×#125 | C2 |
| hypercenter | #125 | D3 |
| hypocenter | C3 | #553 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#125 | C2 | semidirect |
| 2. #898 | C2 | semidirect |
| 3. #895 | C2 | semidirect |
| 4. #895 | C2 | semidirect |
| 5. #895 | C2 | semidirect |
| 6. #894 | C2 | semidirect |
| 7. #893 | C2 | semidirect |
| 8. #892 | C2 | semidirect |
| 9. D3×C4⋊C4 | C2 | semidirect |
| 10. C4×D12 | C2 | semidirect |
| 11. C4×D12 | C2 | semidirect |
| 37. #125 | D3 | semidirect |
| 150. C3 | #553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#125 | 2 |
| #898 | 2 |
| #895 | 2 |
| #894 | 2 |
| #893 | 2 |
| #892 | 2 |
| D3×C4⋊C4 | 2 |
| C4×D12 | 2 |
| #553 | 3 |