Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
310 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 109 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×#121 | C2 |
| hypercenter | #121 | D3 |
| hypocenter | C3 | #532 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#237 | C2 | semidirect |
| 2. C3×#121 | C2 | semidirect |
| 3. #940 | C2 | semidirect |
| 4. #939 | C2 | semidirect |
| 5. D4×Dic3 | C2 | semidirect |
| 6. #930 | C2 | semidirect |
| 7. C2×C4×Dic3 | C2 | semidirect |
| 8. #893 | C2 | semidirect |
| 9. #888 | C2 | semidirect |
| 10. #885 | C2 | semidirect |
| 11. #67⋊C4 | C2 | semidirect |
| 43. #121 | D3 | semidirect |
| 62. C2×Dic3 | D4 | semidirect |
| 107. C3×C4 | #41 | semidirect |
| 112. Dic3 | #41 | semidirect |
| 159. C4 | #237 | semidirect |
| 160. C3 | #532 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#237 | 2 |
| C3×#121 | 2 |
| #940 | 2 |
| #939 | 2 |
| D4×Dic3 | 2 |
| #930 | 2 |
| C2×C4×Dic3 | 2 |
| #893 | 2 |
| #888 | 2 |
| #885 | 2 |
| #67⋊C4 | 2 |
| #532 | 3 |