Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
268 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 99 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. #19149724 | C2 | semidirect |
| 2. #19149705 | C2 | semidirect |
| 3. #19149703 | C2 | semidirect |
| 4. #19149701 | C2 | semidirect |
| 5. #19149698 | C2 | semidirect |
| 6. D8×D173 | C2 | semidirect |
| 7. #19149685 | C2 | semidirect |
| 8. C2×D8×C173 | C2 | semidirect |
| 10. #14583826 | C22 | semidirect |
| 12. #14583825 | C22 | semidirect |
| 15. D4×D173 | C22 | semidirect |
| 16. Dic692 | C22 | semidirect |
| 17. #14583815 | C22 | semidirect |
| 18. #14583814 | C22 | semidirect |
| 19. D1384 | C22 | semidirect |
| 20. #14583811 | C22 | semidirect |
| 21. #14583810 | C22 | semidirect |
| 22. #14583809 | C22 | semidirect |
| 23. C8×D173 | C22 | semidirect |
| 24. C2×D4×C173 | C22 | semidirect |
| 25. D8×C173 | C22 | semidirect |
| 26. D8×C173 | C22 | semidirect |
| 27. C2×C8×C173 | C22 | semidirect |
| 62. C173 | #576 | semidirect |
| 70. C2×D8 | D173 | semidirect |
| 79. C2×D4 | C2×D173 | semidirect |
| 85. D8 | C2×D173 | semidirect |
| 86. D8 | C2×D173 | semidirect |
| 90. C2×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149724 | 2 |
| #19149705 | 2 |
| #19149703 | 2 |
| #19149701 | 2 |
| #19149698 | 2 |
| D8×D173 | 2 |
| #19149685 | 2 |
| C2×D8×C173 | 2 |
| #576 | 173 |