Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
| prime radical | C2×D12 | C22 |
| hypercenter | #125 | D3 |
| hypocenter | C3 | #563 |
| 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. #898 | C2 | semidirect |
| 4. #897 | C2 | semidirect |
| 5. #896 | C2 | semidirect |
| 7. #888 | C2 | semidirect |
| 9. #870 | C2 | semidirect |
| 36. #125 | D3 | semidirect |
| 116. C3 | #563 | 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 |
| #897 | 2 |
| #896 | 2 |
| #894 | 2 |
| #888 | 2 |
| #875 | 2 |
| #870 | 2 |
| #563 | 3 |