Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #22581720 | C2 | semidirect |
| 3. #22580971 | C2 | semidirect |
| 4. C2×#17984770 | C2 | semidirect |
| 5. C4×#41×C139 | C2 | semidirect |
| 7. #17984889 | C4 | semidirect |
| 8. #17984888 | C4 | semidirect |
| 13. C2×#14555769 | C22 | semidirect |
| 14. #17984770 | C22 | semidirect |
| 15. #17984770 | C22 | semidirect |
| 19. #117×C139 | C22 | semidirect |
| 20. C2×C42×C139 | C22 | semidirect |
| 24. #14555785 | C2×C4 | semidirect |
| 27. C2×Dic278 | C2×C4 | semidirect |
| 29. C2×D556 | C2×C4 | semidirect |
| 83. C139 | #2901 | semidirect |
| 87. C4×#41 | D139 | semidirect |
| 101. #117 | C2×D139 | semidirect |
| 102. C2×C42 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581789 | 2 |
| #22581720 | 2 |
| #22580971 | 2 |
| C2×#17984770 | 2 |
| C4×#41×C139 | 2 |
| #2901 | 139 |