Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
310 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Frattini | C22 | C23×D3 |
| Fitting | C2×C3×#41 | C2 |
| hypercenter | C2×#41 | D3 |
| hypocenter | C3 | #532 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#41 | C2 | semidirect |
| 2. C2×#235 | C2 | semidirect |
| 3. #947 | C2 | semidirect |
| 4. #944 | C2 | semidirect |
| 5. #940 | C2 | semidirect |
| 6. #939 | C2 | semidirect |
| 7. #936 | C2 | semidirect |
| 8. C4×#67 | C2 | semidirect |
| 9. C2×C4×Dic3 | C2 | semidirect |
| 31. C2×#41 | D3 | semidirect |
| 46. C2×C3×C4 | D4 | semidirect |
| 90. Dic3 | #41 | semidirect |
| 107. C2×C4 | #67 | semidirect |
| 129. C3 | #532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41 | 2 |
| C2×#235 | 2 |
| #947 | 2 |
| #944 | 2 |
| #940 | 2 |
| #939 | 2 |
| #936 | 2 |
| C4×#67 | 2 |
| C2×C4×Dic3 | 2 |
| #532 | 3 |