Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
778 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 200 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. D149⋊#131 | C2 | semidirect |
| 2. #23750694 | C2 | semidirect |
| 3. #23750617 | C2 | semidirect |
| 4. #23750616 | C2 | semidirect |
| 5. #23750615 | C2 | semidirect |
| 6. C2×#18011973 | C2 | semidirect |
| 10. D149⋊M16 | C22 | semidirect |
| 11. C2×D149⋊C8 | C22 | semidirect |
| 14. #18011990 | C22 | semidirect |
| 15. C2×C4⋊#10597010 | C22 | semidirect |
| 16. #18011974 | C22 | semidirect |
| 17. #18011974 | C22 | semidirect |
| 18. #18011973 | C22 | semidirect |
| 19. #18011973 | C22 | semidirect |
| 20. #18011973 | C22 | semidirect |
| 22. #18011957 | C4 | semidirect |
| 23. #18011957 | C4 | semidirect |
| 25. #18011956 | C4 | semidirect |
| 31. H(5,𝔽2)×C149 | C4 | semidirect |
| 46. #14558737 | C2×C4 | semidirect |
| 51. #14558736 | C2×C4 | semidirect |
| 54. #14558735 | C2×C4 | semidirect |
| 59. C2×D596 | C2×C4 | semidirect |
| 68. D4×D149 | C2×C4 | semidirect |
| 75. #41×C149 | C2×C4 | semidirect |
| 77. C2×D4×C149 | C2×C4 | semidirect |
| 146. C149 | #2897 | semidirect |
| 160. H(5,𝔽2) | #10597010 | semidirect |
| 193. #41 | C2×#10597010 | semidirect |
| 210. C2×D4 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D149⋊#131 | 2 |
| #23750694 | 2 |
| #23750617 | 2 |
| #23750616 | 2 |
| #23750615 | 2 |
| C2×#18011973 | 2 |
| H(5,𝔽2)×D149 | 2 |
| #2897 | 149 |