Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
334 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 334 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 | 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. C2×C3×#41 | C2 | semidirect |
| 2. C22×C3×D4 | C2 | semidirect |
| 3. C3×#127 | C2 | semidirect |
| 4. C3×#124 | C2 | semidirect |
| 5. C3×#121 | C2 | semidirect |
| 6. C3×#120 | C2 | semidirect |
| 7. C3×#117 | C2 | semidirect |
| 8. #535 | C3 | direct (N × H) |
| 11. C2×C3×Q8 | C22 | semidirect |
| 16. C2×C3×D4 | C22 | semidirect |
| 17. C2×C3×D4 | C22 | semidirect |
| 19. C22×C3×C4 | C22 | semidirect |
| 20. C3×C4⋊C4 | C22 | semidirect |
| 22. C3×C22⋊C4 | C22 | semidirect |
| 23. C3×C42 | C22 | semidirect |
| 24. C2×#41 | C2×C3 | semidirect |
| 25. C22×D4 | C2×C3 | semidirect |
| 26. #127 | C2×C3 | semidirect |
| 27. #124 | C2×C3 | semidirect |
| 28. #121 | C2×C3 | semidirect |
| 29. #120 | C2×C3 | semidirect |
| 30. #117 | C2×C3 | semidirect |
| 43. C2×C3×C4 | D4 | semidirect |
| 50. C2×Q8 | C22×C3 | semidirect |
| 55. C2×D4 | C22×C3 | semidirect |
| 56. C2×D4 | C22×C3 | semidirect |
| 58. C22×C4 | C22×C3 | semidirect |
| 59. C4⋊C4 | C22×C3 | semidirect |
| 61. C22⋊C4 | C22×C3 | semidirect |
| 62. C42 | C22×C3 | semidirect |
| 87. C2×C4 | C3×D4 | semidirect |
| 109. C3 | #535 | 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×#127 | 2 |
| C3×#124 | 2 |
| C3×#121 | 2 |
| C3×#120 | 2 |
| C3×#117 | 2 |
| #535 | 3 |