Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #23750704 | C2 | semidirect |
| 2. #41×#10597010 | C2 | semidirect |
| 3. #23750624 | C2 | semidirect |
| 4. #23750622 | C2 | semidirect |
| 5. C2×#18011976 | C2 | semidirect |
| 6. D149⋊#104 | C2 | semidirect |
| 10. C2×#14558746 | C22 | semidirect |
| 11. D149⋊M16 | C22 | semidirect |
| 14. #18011990 | C22 | semidirect |
| 15. C2×C4×#10597010 | C22 | semidirect |
| 16. #18011976 | C22 | semidirect |
| 17. #18011976 | C22 | semidirect |
| 18. #18011976 | C22 | semidirect |
| 19. #18011975 | C22 | semidirect |
| 20. #18011975 | C22 | semidirect |
| 22. #18011959 | C4 | semidirect |
| 24. #18011957 | C4 | semidirect |
| 25. #18011957 | C4 | semidirect |
| 31. 2−1+4×C149 | C4 | semidirect |
| 48. #14558737 | C2×C4 | semidirect |
| 55. #14558736 | C2×C4 | semidirect |
| 60. Q8×D149 | C2×C4 | semidirect |
| 64. C2×D596 | C2×C4 | semidirect |
| 68. D4×D149 | C2×C4 | semidirect |
| 75. #41×C149 | C2×C4 | semidirect |
| 77. C2×Q8×C149 | C2×C4 | semidirect |
| 139. C149 | #2901 | semidirect |
| 150. 2−1+4 | #10597010 | semidirect |
| 189. #41 | C2×#10597010 | semidirect |
| 194. C2×Q8 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750704 | 2 |
| #41×#10597010 | 2 |
| #23750624 | 2 |
| #23750622 | 2 |
| C2×#18011976 | 2 |
| D149⋊#104 | 2 |
| #23750462 | 2 |
| #2901 | 149 |