Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 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 | #67 |
| commutator, cosocle | C3×C4 | C24 |
| Frattini | C4 | C23×D3 |
| Fitting | C2×C3×#41 | C2 |
| socle | C22×C3 | C2×D4 |
| hypercenter | C2×#41 | D3 |
| hypocenter | C3 | C2×#135 |
| LCS | G ▷ C3×C4 ▷ C2×C3 ▷ C3 | |
| UCS | C1 ◁ C2×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. #950 | C2 | direct (N × H) |
| 4. C2×#216 | C2 | semidirect |
| 5. C2×#215 | C2 | semidirect |
| 6. C2×#214 | C2 | semidirect |
| 7. C2×#213 | C2 | semidirect |
| 8. C22×C3⋊C8 | C2 | semidirect |
| 11. C3×#41 | C22 | semidirect |
| 19. #235 | C22 | semidirect |
| 23. #216 | C22 | semidirect |
| 24. #215 | C22 | semidirect |
| 25. #214 | C22 | semidirect |
| 26. #213 | C22 | semidirect |
| 29. C2×C3⋊C8 | C22 | semidirect |
| 31. C2×#41 | D3 | semidirect |
| 64. #41 | C2×D3 | semidirect |
| 118. C2×C3 | #135 | semidirect |
| 133. C3 | C2×#135 | semidirect |
| 137. C2 | #950 | direct (N × H) |
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 |
| #950 | 2 |
| C2×#216 | 2 |
| C2×#215 | 2 |
| C2×#214 | 2 |
| C2×#213 | 2 |
| C22×C3⋊C8 | 2 |
| C2×#135 | 3 |