Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
458 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 2. #22581719 | C2 | semidirect |
| 3. #22581074 | C2 | semidirect |
| 4. #22581069 | C2 | semidirect |
| 5. C2×#17984768 | C2 | semidirect |
| 6. M16×Dic139 | C2 | semidirect |
| 7. #430×C139 | C2 | semidirect |
| 9. #17984875 | C4 | semidirect |
| 10. #17984870 | C4 | semidirect |
| 12. #17984850 | C22 | semidirect |
| 17. #17984768 | C22 | semidirect |
| 18. #17984768 | C22 | semidirect |
| 19. #17984752 | C22 | semidirect |
| 20. C8×Dic139 | C22 | semidirect |
| 23. #108×C139 | C22 | semidirect |
| 33. Dic556 | C2×C4 | semidirect |
| 34. #14555774 | C2×C4 | semidirect |
| 35. D1112 | C2×C4 | semidirect |
| 85. C139 | #2956 | semidirect |
| 91. #430 | D139 | semidirect |
| 105. #108 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581753 | 2 |
| #22581719 | 2 |
| #22581074 | 2 |
| #22581069 | 2 |
| C2×#17984768 | 2 |
| M16×Dic139 | 2 |
| #430×C139 | 2 |
| #2956 | 139 |