Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 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. #23750256 | C2 | semidirect |
| 3. #23749988 | C2 | semidirect |
| 4. #23749986 | C2 | semidirect |
| 5. #23749981 | C2 | semidirect |
| 6. #23749970 | C2 | semidirect |
| 7. #23749631 | C2 | semidirect |
| 8. #23749621 | C2 | semidirect |
| 9. C2×#18011831 | C2 | semidirect |
| 10. #23749583 | C2 | semidirect |
| 11. #417×C149 | C2 | semidirect |
| 15. #18011910 | C22 | semidirect |
| 18. #18011902 | C22 | semidirect |
| 26. #18011835 | C22 | semidirect |
| 27. #18011835 | C22 | semidirect |
| 30. #18011832 | C22 | semidirect |
| 31. #18011832 | C22 | semidirect |
| 34. #18011821 | C22 | semidirect |
| 35. C8×Dic149 | C22 | semidirect |
| 39. #103×C149 | C22 | semidirect |
| 40. #102×C149 | C22 | semidirect |
| 135. C149 | #3136 | semidirect |
| 144. #417 | D149 | semidirect |
| 167. #103 | C2×D149 | semidirect |
| 174. #102 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750256 | 2 |
| #23750189 | 2 |
| #23749988 | 2 |
| #23749986 | 2 |
| #23749981 | 2 |
| #23749970 | 2 |
| #23749631 | 2 |
| #23749621 | 2 |
| C2×#18011831 | 2 |
| #23749583 | 2 |
| #417×C149 | 2 |
| #3136 | 149 |