Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
146 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #882 |
| commutator, cosocle | C2×C3×C4 | C23 |
| Frattini | C2×C4 | C22×D3 |
| Fitting | C3×#104 | C2 |
| socle | C2×C3 | #120 |
| hypercenter | #104 | D3 |
| hypocenter | C3 | #454 |
| LCS | G ▷ C2×C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #104 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #1010 | C2 | semidirect |
| 2. #949 | C2 | semidirect |
| 3. #908 | C2 | semidirect |
| 4. #875 | C2 | semidirect |
| 5. C3×#104 | C2 | semidirect |
| 6. #824 | C2 | semidirect |
| 7. #805 | C2 | semidirect |
| 31. #104 | D3 | semidirect |
| 121. C3 | #454 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #1010 | 2 |
| #949 | 2 |
| #908 | 2 |
| #875 | 2 |
| C3×#104 | 2 |
| #824 | 2 |
| #805 | 2 |
| #454 | 3 |