Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
250 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 146 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 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C3 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#126 | C2 | semidirect |
| 2. C3×#124 | C2 | semidirect |
| 3. C3×#123 | C2 | semidirect |
| 4. C3×C22⋊Q8 | C2 | semidirect |
| 5. C3×#121 | C2 | semidirect |
| 6. C3×#121 | C2 | semidirect |
| 7. C3×#120 | C2 | semidirect |
| 8. C3×C4×D4 | C2 | semidirect |
| 9. C2×C3×C22⋊C4 | C2 | semidirect |
| 10. #538 | C3 | direct (N × H) |
| 12. C2×C3×Q8 | C22 | semidirect |
| 16. C2×C3×D4 | C22 | semidirect |
| 19. C22×C3×C4 | C22 | semidirect |
| 20. C3×C4⋊C4 | C22 | semidirect |
| 21. C3×C4⋊C4 | C22 | semidirect |
| 22. C3×C4⋊C4 | C22 | semidirect |
| 23. C3×C4⋊C4 | C22 | semidirect |
| 29. C3×C22⋊C4 | C22 | semidirect |
| 30. C3×C22⋊C4 | C22 | semidirect |
| 31. C3×C42 | C22 | semidirect |
| 32. #126 | C2×C3 | semidirect |
| 33. #124 | C2×C3 | semidirect |
| 34. #123 | C2×C3 | semidirect |
| 35. C22⋊Q8 | C2×C3 | semidirect |
| 36. #121 | C2×C3 | semidirect |
| 37. #121 | C2×C3 | semidirect |
| 38. #120 | C2×C3 | semidirect |
| 39. C4×D4 | C2×C3 | semidirect |
| 40. C2×C22⋊C4 | C2×C3 | semidirect |
| 62. C2×Q8 | C22×C3 | semidirect |
| 66. C2×D4 | C22×C3 | semidirect |
| 69. C22×C4 | C22×C3 | semidirect |
| 70. C4⋊C4 | C22×C3 | semidirect |
| 71. C4⋊C4 | C22×C3 | semidirect |
| 72. C4⋊C4 | C22×C3 | semidirect |
| 73. C4⋊C4 | C22×C3 | semidirect |
| 79. C22⋊C4 | C22×C3 | semidirect |
| 80. C22⋊C4 | C22×C3 | semidirect |
| 81. C42 | C22×C3 | semidirect |
| 142. C3 | #538 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#126 | 2 |
| C3×#124 | 2 |
| C3×#123 | 2 |
| C3×C22⋊Q8 | 2 |
| C3×#121 | 2 |
| C3×#120 | 2 |
| C3×C4×D4 | 2 |
| C2×C3×C22⋊C4 | 2 |
| #538 | 3 |