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. #23750172 | C2 | semidirect |
| 2. #127×D149 | C2 | semidirect |
| 3. #23750000 | C2 | semidirect |
| 4. #23749970 | C2 | semidirect |
| 5. #23749821 | C2 | semidirect |
| 6. #23749820 | C2 | semidirect |
| 7. #23749817 | C2 | semidirect |
| 8. #23749760 | C2 | semidirect |
| 9. #23749757 | C2 | semidirect |
| 10. #23749677 | C2 | semidirect |
| 11. #459×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 |
| 29. C4×D596 | C22 | semidirect |
| 32. C4⋊#11924746 | C22 | semidirect |
| 33. #18011833 | C22 | semidirect |
| 34. #18011832 | C22 | semidirect |
| 35. #18011831 | C22 | semidirect |
| 37. C8×Dic149 | C22 | semidirect |
| 38. C2×D8×C149 | C22 | semidirect |
| 40. C4×D4×C149 | C22 | semidirect |
| 41. C4⋊C8×C149 | C22 | semidirect |
| 42. #102×C149 | C22 | semidirect |
| 115. C4×D149 | D8 | semidirect |
| 165. C149 | #3205 | semidirect |
| 174. #459 | D149 | semidirect |
| 185. C2×D8 | C2×D149 | semidirect |
| 199. C4×D4 | C2×D149 | semidirect |
| 202. C4⋊C8 | C2×D149 | semidirect |
| 206. #102 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750172 | 2 |
| #127×D149 | 2 |
| #23750000 | 2 |
| #23749970 | 2 |
| #23749821 | 2 |
| #23749820 | 2 |
| #23749817 | 2 |
| #23749760 | 2 |
| #23749757 | 2 |
| #23749677 | 2 |
| #459×C149 | 2 |
| #3205 | 149 |