Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #19149726 | C2 | semidirect |
| 2. #19149725 | C2 | semidirect |
| 3. #19149712 | C2 | semidirect |
| 4. #19149707 | C2 | semidirect |
| 5. #19149701 | C2 | semidirect |
| 6. C2×#14583815 | C2 | semidirect |
| 7. #131×C173 | C2 | semidirect |
| 10. #14583826 | C22 | semidirect |
| 12. C2×Dic346 | C22 | semidirect |
| 16. Dic692 | C22 | semidirect |
| 17. #14583815 | C22 | semidirect |
| 18. #14583815 | C22 | semidirect |
| 19. #14583815 | C22 | semidirect |
| 20. D1384 | C22 | semidirect |
| 22. M16×C173 | C22 | semidirect |
| 23. C2×C8×C173 | C22 | semidirect |
| 53. C173 | #577 | semidirect |
| 61. #131 | D173 | semidirect |
| 76. M16 | C2×D173 | semidirect |
| 77. C2×C8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149726 | 2 |
| #19149725 | 2 |
| #19149712 | 2 |
| #19149707 | 2 |
| #19149701 | 2 |
| C2×#14583815 | 2 |
| #131×C173 | 2 |
| #577 | 173 |