Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22581291 | C2 | semidirect |
| 3. #22581250 | C2 | semidirect |
| 4. #22581155 | C2 | semidirect |
| 6. #22581051 | C2 | semidirect |
| 7. C4×#14555772 | C2 | semidirect |
| 8. #22581014 | C2 | semidirect |
| 9. #541×C139 | C2 | semidirect |
| 18. #17984775 | C22 | semidirect |
| 19. #17984773 | C22 | semidirect |
| 20. C4⋊(C139⋊C8) | C22 | semidirect |
| 21. #17984766 | C22 | semidirect |
| 22. #17984766 | C22 | semidirect |
| 26. #17984753 | C22 | semidirect |
| 27. C4×C139⋊C8 | C22 | semidirect |
| 28. C4⋊Q8×C139 | C22 | semidirect |
| 31. #125×C139 | C22 | semidirect |
| 33. C4×Q8×C139 | C22 | semidirect |
| 102. C139 | #3123 | semidirect |
| 104. #541 | D139 | semidirect |
| 116. C4⋊Q8 | C2×D139 | semidirect |
| 119. #125 | C2×D139 | semidirect |
| 121. C4×Q8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581427 | 2 |
| #22581291 | 2 |
| #22581250 | 2 |
| #22581155 | 2 |
| #22581103 | 2 |
| #22581051 | 2 |
| C4×#14555772 | 2 |
| #22581014 | 2 |
| #541×C139 | 2 |
| #3123 | 139 |