Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
488 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 488 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. #23750177 | C2 | semidirect |
| 3. #23749996 | C2 | semidirect |
| 4. #23749970 | C2 | semidirect |
| 5. #23749824 | C2 | semidirect |
| 6. #23749823 | C2 | semidirect |
| 7. #23749778 | C2 | semidirect |
| 8. #23749776 | C2 | semidirect |
| 9. #23749775 | C2 | semidirect |
| 10. #23749675 | C2 | semidirect |
| 11. #450×C149 | C2 | semidirect |
| 15. C2×#14558725 | C22 | semidirect |
| 16. C2×#14558724 | C22 | semidirect |
| 17. C2×#14558723 | C22 | semidirect |
| 18. #18011910 | C22 | semidirect |
| 19. #18011909 | C22 | semidirect |
| 27. Q8×Dic149 | C22 | semidirect |
| 29. #18011876 | 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×SD16×C149 | C22 | semidirect |
| 41. #102×C149 | C22 | semidirect |
| 102. C2×Dic149 | SD16 | semidirect |
| 151. C149 | #3208 | semidirect |
| 162. #450 | D149 | semidirect |
| 171. C2×SD16 | C2×D149 | semidirect |
| 191. #102 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750177 | 2 |
| C2×#18011907 | 2 |
| #23749996 | 2 |
| #23749970 | 2 |
| #23749824 | 2 |
| #23749823 | 2 |
| #23749778 | 2 |
| #23749776 | 2 |
| #23749775 | 2 |
| #23749675 | 2 |
| #450×C149 | 2 |
| #3208 | 149 |