Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
532 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23750170 | C2 | semidirect |
| 2. C2×#18011907 | C2 | semidirect |
| 3. #23750000 | C2 | semidirect |
| 4. #23749970 | C2 | semidirect |
| 5. #23749819 | C2 | semidirect |
| 6. #23749818 | C2 | semidirect |
| 7. #23749761 | C2 | semidirect |
| 8. #23749759 | C2 | semidirect |
| 9. #23749758 | C2 | semidirect |
| 10. #23749675 | C2 | semidirect |
| 11. #447×C149 | C2 | semidirect |
| 16. C2×D1192 | C22 | semidirect |
| 17. C2×#14558721 | C22 | semidirect |
| 18. C2×#14558721 | C22 | semidirect |
| 19. #18011910 | C22 | semidirect |
| 24. #18011907 | C22 | semidirect |
| 28. D4×Dic149 | C22 | semidirect |
| 29. #18011873 | C22 | semidirect |
| 32. #18011840 | C22 | semidirect |
| 33. #18011833 | C22 | semidirect |
| 34. #18011832 | C22 | semidirect |
| 35. #18011831 | C22 | semidirect |
| 37. C8×Dic149 | C22 | semidirect |
| 39. C2×D8×C149 | C22 | semidirect |
| 41. #102×C149 | C22 | semidirect |
| 107. C2×Dic149 | D8 | semidirect |
| 164. C149 | #3205 | semidirect |
| 175. #447 | D149 | semidirect |
| 185. C2×D8 | C2×D149 | semidirect |
| 204. #102 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750170 | 2 |
| C2×#18011907 | 2 |
| #23750000 | 2 |
| #23749970 | 2 |
| #23749819 | 2 |
| #23749818 | 2 |
| #23749761 | 2 |
| #23749759 | 2 |
| #23749758 | 2 |
| #23749675 | 2 |
| #447×C149 | 2 |
| #3205 | 149 |