Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×#67 |
| commutator, cosocle | C3×C4 | C24 |
| Frattini | C4 | C23×D3 |
| Fitting | C2×C3×#41 | C2 |
| socle | C2×C3 | C22×D4 |
| hypercenter | C2×#41 | D3 |
| hypocenter | C3 | #575 |
| LCS | G ▷ C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C4 ◁ C22×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. #951 | C2 | semidirect |
| 4. #950 | C2 | semidirect |
| 5. #949 | C2 | semidirect |
| 6. #942 | C2 | semidirect |
| 7. #932 | C2 | semidirect |
| 8. C2×#208 | C2 | semidirect |
| 13. C3×#41 | C22 | semidirect |
| 14. C2×C3×Q8 | C22 | semidirect |
| 16. C2×C3×D4 | C22 | semidirect |
| 23. #235 | C22 | semidirect |
| 24. C2×D12 | C22 | semidirect |
| 26. C2×Dic6 | C22 | semidirect |
| 27. #216 | C22 | semidirect |
| 28. #215 | C22 | semidirect |
| 29. #214 | C22 | semidirect |
| 30. #213 | C22 | semidirect |
| 31. #208 | C22 | semidirect |
| 32. #208 | C22 | semidirect |
| 33. C2×C3⋊C8 | C22 | semidirect |
| 35. C2×#41 | D3 | semidirect |
| 77. #41 | C2×D3 | semidirect |
| 79. C2×Q8 | C2×D3 | semidirect |
| 83. C2×D4 | C2×D3 | semidirect |
| 156. C3 | #575 | 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 |
| #951 | 2 |
| #950 | 2 |
| #949 | 2 |
| #942 | 2 |
| #932 | 2 |
| C2×#208 | 2 |
| #575 | 3 |