Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
370 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22581758 | C2 | semidirect |
| 2. #22581389 | C2 | semidirect |
| 3. #22581388 | C2 | semidirect |
| 4. #22581383 | C2 | semidirect |
| 5. C2×#17984783 | C2 | semidirect |
| 6. #22581370 | C2 | semidirect |
| 7. #576×C139 | C2 | semidirect |
| 10. #17984864 | C22 | semidirect |
| 11. C2×D1112 | C22 | semidirect |
| 12. #17984788 | C22 | semidirect |
| 13. #17984786 | C22 | semidirect |
| 14. #17984785 | C22 | semidirect |
| 15. #17984783 | C22 | semidirect |
| 16. #17984783 | C22 | semidirect |
| 17. #17984782 | C22 | semidirect |
| 18. C2×C139⋊C16 | C22 | semidirect |
| 21. #135×C139 | C22 | semidirect |
| 22. C2×D8×C139 | C22 | semidirect |
| 75. C139 | #3415 | semidirect |
| 78. #576 | D139 | semidirect |
| 89. #135 | C2×D139 | semidirect |
| 91. C2×D8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581758 | 2 |
| #22581389 | 2 |
| #22581388 | 2 |
| #22581383 | 2 |
| C2×#17984783 | 2 |
| #22581370 | 2 |
| #576×C139 | 2 |
| #3415 | 139 |