Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23750136 | C2 | semidirect |
| 2. C2×#18011885 | C2 | semidirect |
| 3. #23749961 | C2 | semidirect |
| 4. #23749950 | C2 | semidirect |
| 5. #23749944 | C2 | semidirect |
| 6. #23749861 | C2 | semidirect |
| 7. #23749854 | C2 | semidirect |
| 8. #23749778 | C2 | semidirect |
| 9. #23749772 | C2 | semidirect |
| 10. #23749761 | C2 | semidirect |
| 11. C2×C22⋊C8×C149 | C2 | semidirect |
| 12. C2×#14558736 | C22 | semidirect |
| 15. C2×#14558725 | C22 | semidirect |
| 16. C2×D1192 | C22 | semidirect |
| 19. #18011890 | C22 | semidirect |
| 25. #18011885 | C22 | semidirect |
| 29. #18011870 | C22 | semidirect |
| 32. #18011845 | C22 | semidirect |
| 33. #18011843 | C22 | semidirect |
| 34. #18011836 | C22 | semidirect |
| 35. #18011833 | C22 | semidirect |
| 36. #18011833 | C22 | semidirect |
| 37. #18011833 | C22 | semidirect |
| 39. C22×C8×C149 | C22 | semidirect |
| 42. C22⋊C8×C149 | C22 | semidirect |
| 158. C149 | #3188 | semidirect |
| 170. C2×C22⋊C8 | D149 | semidirect |
| 177. C22×C8 | C2×D149 | semidirect |
| 201. C22⋊C8 | C2×D149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750136 | 2 |
| C2×#18011885 | 2 |
| #23749961 | 2 |
| #23749950 | 2 |
| #23749944 | 2 |
| #23749861 | 2 |
| #23749854 | 2 |
| #23749778 | 2 |
| #23749772 | 2 |
| #23749761 | 2 |
| C2×C22⋊C8×C149 | 2 |
| #3188 | 149 |