Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
364 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 364 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. C2×#17984864 | C2 | semidirect |
| 2. #22581394 | C2 | semidirect |
| 3. #22581393 | C2 | semidirect |
| 4. #22581389 | C2 | semidirect |
| 5. #22581388 | C2 | semidirect |
| 6. #22581383 | C2 | semidirect |
| 7. C2×#17984782 | C2 | semidirect |
| 8. C2×#135×C139 | C2 | semidirect |
| 13. #17984864 | C22 | semidirect |
| 14. C2×Dic556 | C22 | semidirect |
| 16. C2×D1112 | C22 | semidirect |
| 17. #17984788 | C22 | semidirect |
| 18. #17984786 | C22 | semidirect |
| 19. #17984785 | C22 | semidirect |
| 20. #17984783 | C22 | semidirect |
| 21. #17984782 | C22 | semidirect |
| 22. #17984782 | C22 | semidirect |
| 23. C2×C139⋊C16 | C22 | semidirect |
| 28. #135×C139 | C22 | semidirect |
| 29. C2×Q16×C139 | C22 | semidirect |
| 31. C2×D8×C139 | C22 | semidirect |
| 120. C139 | #3414 | semidirect |
| 123. C2×#135 | D139 | semidirect |
| 139. #135 | C2×D139 | semidirect |
| 141. C2×Q16 | C2×D139 | semidirect |
| 145. C2×D8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984864 | 2 |
| #22581394 | 2 |
| #22581393 | 2 |
| #22581389 | 2 |
| #22581388 | 2 |
| #22581383 | 2 |
| C2×#17984782 | 2 |
| C2×#135×C139 | 2 |
| #3414 | 139 |