Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
170 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C4 | D4 |
| commutator | C4 | C22×C3×C4 |
| Frattini, cosocle | C2×C4 | C23×C3 |
| socle | C22×C3 | C22⋊C4 |
| prime radical | C2×C3×#41 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C4 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C3×M16 | C2 | semidirect |
| 3. C2×C3×C42 | C2 | semidirect |
| 4. C3×#104 | C2 | direct (N × H) |
| 5. C2×#104 | C3 | direct (N × H) |
| 8. C3×#41 | C4 | semidirect |
| 10. C2×C3×Q8 | C4 | semidirect |
| 12. C2×C3×D4 | C4 | semidirect |
| 17. C3×M16 | C22 | semidirect |
| 20. C3×C42 | C22 | semidirect |
| 22. C2×M16 | C2×C3 | semidirect |
| 23. C2×C42 | C2×C3 | semidirect |
| 24. #104 | C2×C3 | direct (N × H) |
| 28. C3×Q8 | C2×C4 | semidirect |
| 32. C3×D4 | C2×C4 | semidirect |
| 47. #41 | C3×C4 | semidirect |
| 49. C2×Q8 | C3×C4 | semidirect |
| 51. C2×D4 | C3×C4 | semidirect |
| 56. M16 | C22×C3 | semidirect |
| 59. C42 | C22×C3 | semidirect |
| 75. Q8 | C2×C3×C4 | semidirect |
| 79. D4 | C2×C3×C4 | semidirect |
| 95. C2×C3 | #104 | direct (N × H) |
| 109. C3 | C2×#104 | direct (N × H) |
| 113. C2 | C3×#104 | 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×C3×M16 | 2 |
| C2×C3×C42 | 2 |
| C3×#104 | 2 |
| C2×#104 | 3 |