Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17984868 | C2 | semidirect |
| 2. C2×#17984864 | C2 | semidirect |
| 3. #22581520 | C2 | semidirect |
| 4. #22581341 | C2 | semidirect |
| 5. #22581336 | C2 | semidirect |
| 6. #22581328 | C2 | semidirect |
| 7. #22580908 | C2 | semidirect |
| 8. C22×D8×C139 | C2 | semidirect |
| 12. C2×Dic556 | C22 | semidirect |
| 13. C2×#14555774 | C22 | semidirect |
| 14. C2×#14555773 | C22 | semidirect |
| 15. C2×D1112 | C22 | semidirect |
| 16. C2×#14555770 | C22 | semidirect |
| 18. #17984838 | C22 | semidirect |
| 19. #17984829 | C22 | semidirect |
| 23. #17984752 | C22 | semidirect |
| 24. C8×Dic139 | C22 | semidirect |
| 42. #14555769 | D4 | semidirect |
| 56. C2×C8×C139 | D4 | semidirect |
| 101. C139 | #3155 | semidirect |
| 105. C22×D8 | D139 | semidirect |
| 154. C2×C8 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984868 | 2 |
| C2×#17984864 | 2 |
| #22581520 | 2 |
| #22581341 | 2 |
| #22581336 | 2 |
| #22581328 | 2 |
| #22580908 | 2 |
| C22×D8×C139 | 2 |
| #3155 | 139 |