Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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×C22⋊Q8 | C2 |
| prime radical | #882 | C2 |
| hypercenter | C22⋊Q8 | D3 |
| hypocenter | C3 | #551 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C22⋊Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×C22⋊Q8 | C2 | semidirect |
| 2. #947 | C2 | semidirect |
| 3. #946 | C2 | semidirect |
| 4. C4×#67 | C2 | semidirect |
| 5. C2×(C2×D3)⋊C4 | C2 | semidirect |
| 6. #898 | C2 | semidirect |
| 7. #898 | C2 | semidirect |
| 8. #894 | C2 | semidirect |
| 9. #894 | C2 | semidirect |
| 10. #893 | C2 | semidirect |
| 11. #892 | C2 | semidirect |
| 12. #886 | C2 | semidirect |
| 14. D3×C22⋊C4 | C2 | semidirect |
| 15. #877 | C2 | semidirect |
| 18. C2×C3×Q8 | C22 | semidirect |
| 26. C2×C4×D3 | C22 | semidirect |
| 27. C3×C4⋊C4 | C22 | semidirect |
| 28. C3×C4⋊C4 | C22 | semidirect |
| 29. C3×C4⋊C4 | C22 | semidirect |
| 41. (C2×D3)⋊C4 | C22 | semidirect |
| 42. (C2×D3)⋊C4 | C22 | semidirect |
| 43. (C2×D3)⋊C4 | C22 | semidirect |
| 44. C4⋊Dic3 | C22 | semidirect |
| 45. C4⋊Dic3 | C22 | semidirect |
| 46. Dic3⋊C4 | C22 | semidirect |
| 47. Dic3⋊C4 | C22 | semidirect |
| 48. Dic3⋊C4 | C22 | semidirect |
| 49. C4×Dic3 | C22 | semidirect |
| 50. C4×Dic3 | C22 | semidirect |
| 51. C4×Dic3 | C22 | semidirect |
| 59. C22⋊Q8 | D3 | semidirect |
| 95. C2×Q8 | C2×D3 | semidirect |
| 109. C4⋊C4 | C2×D3 | semidirect |
| 110. C4⋊C4 | C2×D3 | semidirect |
| 111. C4⋊C4 | C2×D3 | semidirect |
| 213. C3 | #551 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C22⋊Q8 | 2 |
| #947 | 2 |
| #946 | 2 |
| C4×#67 | 2 |
| C2×(C2×D3)⋊C4 | 2 |
| #898 | 2 |
| #894 | 2 |
| #893 | 2 |
| #892 | 2 |
| #886 | 2 |
| #882 | 2 |
| D3×C22⋊C4 | 2 |
| #877 | 2 |
| #551 | 3 |