Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #23750102 | C2 | semidirect |
| 4. #23749727 | C2 | semidirect |
| 5. C4×#14558725 | C2 | semidirect |
| 6. #23749663 | C2 | semidirect |
| 7. #23749635 | C2 | semidirect |
| 9. #405×C149 | C2 | semidirect |
| 12. C2×#14558725 | C4 | semidirect |
| 15. C4×Dic298 | C22 | semidirect |
| 23. #18011845 | C22 | semidirect |
| 24. #18011843 | C22 | semidirect |
| 25. #18011836 | C22 | semidirect |
| 30. #97×C149 | C22 | semidirect |
| 31. C4×C8×C149 | C22 | semidirect |
| 35. C2×Dic298 | C2×C4 | semidirect |
| 43. #14558725 | C2×C4 | semidirect |
| 44. #14558725 | C2×C4 | semidirect |
| 56. C2×C8×C149 | C2×C4 | semidirect |
| 103. C149 | #2949 | semidirect |
| 113. #405 | D149 | semidirect |
| 134. #97 | C2×D149 | semidirect |
| 135. C4×C8 | C2×D149 | semidirect |
| 151. C2×C8 | C4×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558725 | 2 |
| #23750102 | 2 |
| #23750099 | 2 |
| #23749727 | 2 |
| C4×#14558725 | 2 |
| #23749663 | 2 |
| #23749635 | 2 |
| #23749631 | 2 |
| #405×C149 | 2 |
| #2949 | 149 |