Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
450 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #23750159 | C2 | semidirect |
| 2. C2×C4×D596 | C2 | semidirect |
| 3. #23749956 | C2 | semidirect |
| 4. #23749939 | C2 | semidirect |
| 5. #23749926 | C2 | semidirect |
| 6. #23749841 | C2 | semidirect |
| 7. #23749778 | C2 | semidirect |
| 9. #23749738 | C2 | semidirect |
| 10. #23749727 | C2 | semidirect |
| 11. #432×C149 | C2 | semidirect |
| 17. #18011903 | C22 | semidirect |
| 18. #18011899 | C22 | semidirect |
| 22. C4×Dic298 | C22 | semidirect |
| 27. C4×D596 | C22 | semidirect |
| 32. #18011845 | C22 | semidirect |
| 33. #18011843 | C22 | semidirect |
| 34. #18011836 | C22 | semidirect |
| 37. #18011833 | C22 | semidirect |
| 39. C4⋊C8×C149 | C22 | semidirect |
| 42. #97×C149 | C22 | semidirect |
| 140. C149 | #3114 | semidirect |
| 152. #432 | D149 | semidirect |
| 176. C4⋊C8 | C2×D149 | semidirect |
| 183. #97 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750159 | 2 |
| C2×C4×D596 | 2 |
| #23749956 | 2 |
| #23749939 | 2 |
| #23749926 | 2 |
| #23749841 | 2 |
| #23749778 | 2 |
| #23749761 | 2 |
| #23749738 | 2 |
| #23749727 | 2 |
| #432×C149 | 2 |
| #3114 | 149 |