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. #19149725 | C2 | semidirect |
| 2. #19149710 | C2 | semidirect |
| 3. #19149704 | C2 | semidirect |
| 4. #19149699 | C2 | semidirect |
| 5. C2×#14583813 | C2 | semidirect |
| 6. #19149686 | C2 | semidirect |
| 7. 2−1+4×C173 | C2 | semidirect |
| 12. #14583816 | C22 | semidirect |
| 13. #14583814 | C22 | semidirect |
| 14. #14583813 | C22 | semidirect |
| 15. #14583813 | C22 | semidirect |
| 16. #14583811 | C22 | semidirect |
| 17. #14583810 | C22 | semidirect |
| 18. C2×#13063436 | C22 | semidirect |
| 21. #41×C173 | C22 | semidirect |
| 23. C2×Q8×C173 | C22 | semidirect |
| 53. C173 | #577 | semidirect |
| 55. 2−1+4 | D173 | semidirect |
| 66. #41 | C2×D173 | semidirect |
| 68. C2×Q8 | C2×D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19149725 | 2 |
| #19149710 | 2 |
| #19149704 | 2 |
| #19149699 | 2 |
| C2×#14583813 | 2 |
| #19149686 | 2 |
| 2−1+4×C173 | 2 |
| #577 | 173 |