Finite Group DatabasebetaFinite Group DatabasebetaOrder 192.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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 | C2×C3×C22⋊C4 | C2 |
| prime radical | #953 | C2 |
| hypercenter | C2×C22⋊C4 | D3 |
| hypocenter | C3 | #551 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C22 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×C22⋊C4 | C2 | semidirect |
| 3. C2×#217 | C2 | semidirect |
| 4. #929 | C2 | semidirect |
| 5. C4×#67 | C2 | semidirect |
| 6. #926 | C2 | semidirect |
| 7. #924 | C2 | semidirect |
| 8. #886 | C2 | semidirect |
| 9. #885 | C2 | semidirect |
| 10. #883 | C2 | semidirect |
| 11. #67⋊C4 | C2 | semidirect |
| 12. #879 | C2 | semidirect |
| 13. #879 | C2 | semidirect |
| 14. #878 | C2 | semidirect |
| 15. #877 | C2 | semidirect |
| 25. C2×C4×D3 | C22 | semidirect |
| 26. C2×Dic6 | C22 | semidirect |
| 38. (C2×D3)⋊C4 | C22 | semidirect |
| 39. (C2×D3)⋊C4 | C22 | semidirect |
| 40. (C2×D3)⋊C4 | C22 | semidirect |
| 41. C4⋊Dic3 | C22 | semidirect |
| 42. C4⋊Dic3 | C22 | semidirect |
| 43. C4⋊Dic3 | C22 | semidirect |
| 44. Dic3⋊C4 | C22 | semidirect |
| 45. Dic3⋊C4 | 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 |
| 66. C2×C22⋊C4 | 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 |
|---|---|
| C2×C3×C22⋊C4 | 2 |
| #953 | 2 |
| C2×#217 | 2 |
| #929 | 2 |
| C4×#67 | 2 |
| #926 | 2 |
| #924 | 2 |
| #886 | 2 |
| #885 | 2 |
| #883 | 2 |
| #67⋊C4 | 2 |
| #879 | 2 |
| #878 | 2 |
| #877 | 2 |
| #551 | 3 |