Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 95 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 | C3×C4×D4 | C2 |
| hypercenter | C4×D4 | D3 |
| hypocenter | C3 | #538 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C4×D4 | C2 | semidirect |
| 2. #939 | C2 | semidirect |
| 3. #937 | C2 | semidirect |
| 4. #930 | C2 | semidirect |
| 5. #929 | C2 | semidirect |
| 6. C4×#67 | C2 | semidirect |
| 7. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 8. #898 | C2 | semidirect |
| 9. #894 | C2 | semidirect |
| 10. #885 | C2 | semidirect |
| 11. #884 | C2 | semidirect |
| 12. #882 | C2 | semidirect |
| 13. #878 | C2 | semidirect |
| 14. #876 | C2 | semidirect |
| 15. #875 | C2 | semidirect |
| 20. C22×C3×C4 | C22 | semidirect |
| 24. C2×#67 | C22 | semidirect |
| 28. C2×C4×D3 | C22 | semidirect |
| 29. C2×Dic6 | C22 | semidirect |
| 30. C3×C4⋊C4 | C22 | semidirect |
| 32. C3×C22⋊C4 | C22 | semidirect |
| 33. C3×C42 | C22 | semidirect |
| 35. #217 | C22 | semidirect |
| 44. (C2×D3)⋊C4 | C22 | semidirect |
| 45. (C2×D3)⋊C4 | C22 | semidirect |
| 46. C4⋊Dic3 | C22 | semidirect |
| 47. Dic3⋊C4 | C22 | semidirect |
| 48. Dic3⋊C4 | C22 | semidirect |
| 49. Dic3⋊C4 | C22 | semidirect |
| 50. Dic3⋊C4 | C22 | semidirect |
| 51. C4×Dic3 | C22 | semidirect |
| 65. C4×D4 | D3 | semidirect |
| 109. C22×C4 | C2×D3 | semidirect |
| 115. C4⋊C4 | C2×D3 | semidirect |
| 129. C22⋊C4 | C2×D3 | semidirect |
| 131. C42 | C2×D3 | semidirect |
| 224. C3 | #538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D4 | 2 |
| #939 | 2 |
| #937 | 2 |
| #930 | 2 |
| #929 | 2 |
| C4×#67 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| #898 | 2 |
| #894 | 2 |
| #885 | 2 |
| #884 | 2 |
| #882 | 2 |
| #878 | 2 |
| #876 | 2 |
| #875 | 2 |
| #538 | 3 |