Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
428 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D3 |
| commutator, socle, cosocle | C22×C3 | C24 |
| Fitting | C22×C3×D4 | C2 |
| hypercenter | C22×D4 | D3 |
| hypocenter | C3 | D42 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×D4 | C2 | semidirect |
| 2. C22×#67 | C2 | semidirect |
| 3. C2×D3×D4 | C2 | semidirect |
| 4. #953 | C2 | semidirect |
| 5. #940 | C2 | semidirect |
| 6. #939 | C2 | semidirect |
| 7. #938 | C2 | semidirect |
| 8. #937 | C2 | semidirect |
| 9. D4×Dic3 | C2 | semidirect |
| 10. #930 | C2 | semidirect |
| 11. C4×#67 | C2 | semidirect |
| 13. C24×C3 | C22 | semidirect |
| 14. C23×D3 | C22 | semidirect |
| 17. C2×C3×D4 | C22 | semidirect |
| 18. C2×C3×D4 | C22 | semidirect |
| 19. C22×C3×C4 | C22 | semidirect |
| 22. C2×#67 | C22 | semidirect |
| 23. C2×#67 | C22 | semidirect |
| 24. C2×#67 | C22 | semidirect |
| 25. C2×#67 | C22 | semidirect |
| 26. C2×#67 | C22 | semidirect |
| 27. C22×Dic3 | C22 | semidirect |
| 29. C2×D12 | C22 | semidirect |
| 30. C2×C4×D3 | C22 | semidirect |
| 31. #217 | C22 | semidirect |
| 32. #217 | C22 | semidirect |
| 33. #217 | C22 | semidirect |
| 34. (C2×D3)⋊C4 | C22 | semidirect |
| 35. (C2×D3)⋊C4 | C22 | semidirect |
| 36. C4⋊Dic3 | C22 | semidirect |
| 37. Dic3⋊C4 | C22 | semidirect |
| 38. C4×Dic3 | C22 | semidirect |
| 41. C22×D4 | D3 | semidirect |
| 63. C3×D4 | D4 | semidirect |
| 72. #67 | D4 | direct (N × H) |
| 81. C24 | C2×D3 | semidirect |
| 93. C2×D4 | C2×D3 | semidirect |
| 94. C2×D4 | C2×D3 | semidirect |
| 97. C22×C4 | C2×D3 | semidirect |
| 114. C22×C3 | C2×D4 | semidirect |
| 115. C22×C3 | C2×D4 | semidirect |
| 123. C2×D3 | C2×D4 | semidirect |
| 125. C3×C4 | C2×D4 | semidirect |
| 129. Dic3 | C2×D4 | semidirect |
| 150. D4 | #67 | direct (N × H) |
| 183. C22 | D3×D4 | semidirect |
| 184. C22 | C2×#67 | semidirect |
| 191. C4 | C2×#67 | semidirect |
| 192. C3 | D42 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D4 | 2 |
| C22×#67 | 2 |
| C2×D3×D4 | 2 |
| #953 | 2 |
| #940 | 2 |
| #939 | 2 |
| #938 | 2 |
| #937 | 2 |
| D4×Dic3 | 2 |
| #930 | 2 |
| C4×#67 | 2 |
| D42 | 3 |