Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
398 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 398 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. #22581581 | C2 | semidirect |
| 2. #22581253 | C2 | semidirect |
| 3. #22581253 | C2 | semidirect |
| 4. #22581243 | C2 | semidirect |
| 5. #22581233 | C2 | semidirect |
| 6. #22580996 | C2 | semidirect |
| 7. #22580989 | C2 | semidirect |
| 8. #22580980 | C2 | semidirect |
| 14. #17984842 | C22 | semidirect |
| 16. #17984834 | C22 | semidirect |
| 21. #17984775 | C22 | semidirect |
| 22. #17984775 | C22 | semidirect |
| 23. #17984775 | C22 | semidirect |
| 24. #17984773 | C22 | semidirect |
| 25. #17984773 | C22 | semidirect |
| 26. #17984773 | C22 | semidirect |
| 27. C4⋊(C139⋊C8) | C22 | semidirect |
| 28. C4⋊(C139⋊C8) | C22 | semidirect |
| 60. C2×D4×C139 | Q8 | semidirect |
| 124. C139 | #3081 | semidirect |
| 170. C2×D4 | Dic278 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581581 | 2 |
| #22581253 | 2 |
| #22581243 | 2 |
| #22581233 | 2 |
| #22580996 | 2 |
| #22580989 | 2 |
| #22580980 | 2 |
| #22580958 | 2 |
| C2×#17984763 | 2 |
| #518×C139 | 2 |
| #3081 | 139 |