Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
298 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3 | C2×D4 |
| commutator, Frattini, cosocle | C4 | C24×C3 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ C22×C3×C4 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×#41 | C2 | semidirect |
| 2. C22×C3×D4 | C2 | semidirect |
| 3. C3×AGL(1,ℤ/8) | C2 | direct (N × H) |
| 4. C2×C3×SD16 | C2 | semidirect |
| 5. C2×C3×D8 | C2 | semidirect |
| 6. C2×C3×M16 | C2 | semidirect |
| 7. C2×AGL(1,ℤ/8) | C3 | direct (N × H) |
| 10. C3×#41 | C22 | semidirect |
| 11. C2×C3×Q8 | C22 | semidirect |
| 16. C2×C3×D4 | C22 | semidirect |
| 17. C2×C3×D4 | C22 | semidirect |
| 20. C3×SD16 | C22 | semidirect |
| 21. C3×D8 | C22 | semidirect |
| 22. C3×M16 | C22 | semidirect |
| 23. C2×C3×C8 | C22 | semidirect |
| 24. C2×#41 | C2×C3 | semidirect |
| 25. C22×D4 | C2×C3 | semidirect |
| 26. AGL(1,ℤ/8) | C2×C3 | direct (N × H) |
| 27. C2×SD16 | C2×C3 | semidirect |
| 28. C2×D8 | C2×C3 | semidirect |
| 29. C2×M16 | C2×C3 | semidirect |
| 36. C3×Q8 | C23 | semidirect |
| 42. C3×D4 | C23 | semidirect |
| 49. C3×C8 | C23 | semidirect |
| 52. #41 | C22×C3 | semidirect |
| 53. C2×Q8 | C22×C3 | semidirect |
| 58. C2×D4 | C22×C3 | semidirect |
| 59. C2×D4 | C22×C3 | semidirect |
| 62. SD16 | C22×C3 | semidirect |
| 63. D8 | C22×C3 | semidirect |
| 64. M16 | C22×C3 | semidirect |
| 65. C2×C8 | C22×C3 | semidirect |
| 84. Q8 | C23×C3 | semidirect |
| 90. D4 | C23×C3 | semidirect |
| 97. C8 | C23×C3 | semidirect |
| 101. C2×C3 | AGL(1,ℤ/8) | direct (N × H) |
| 115. C3 | C2×AGL(1,ℤ/8) | direct (N × H) |
| 119. C2 | C3×AGL(1,ℤ/8) | 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 |
| C22×C3×D4 | 2 |
| C3×AGL(1,ℤ/8) | 2 |
| C2×C3×SD16 | 2 |
| C2×C3×D8 | 2 |
| C2×C3×M16 | 2 |
| C2×AGL(1,ℤ/8) | 3 |