Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #22581510 | C2 | semidirect |
| 3. #22581289 | C2 | semidirect |
| 4. #22581234 | C2 | semidirect |
| 5. #22581159 | C2 | semidirect |
| 7. #22581055 | C2 | semidirect |
| 8. #432×C139 | C2 | semidirect |
| 12. #17984842 | C22 | semidirect |
| 13. #17984842 | C22 | semidirect |
| 18. C4×Dic278 | C22 | semidirect |
| 26. #17984776 | C22 | semidirect |
| 27. #17984767 | C22 | semidirect |
| 30. C4⋊C8×C139 | C22 | semidirect |
| 32. #97×C139 | C22 | semidirect |
| 112. C139 | #3110 | semidirect |
| 121. #432 | D139 | semidirect |
| 141. C4⋊C8 | C2×D139 | semidirect |
| 145. #97 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581510 | 2 |
| C2×C4×D556 | 2 |
| #22581289 | 2 |
| #22581234 | 2 |
| #22581159 | 2 |
| #22581106 | 2 |
| #22581055 | 2 |
| #432×C139 | 2 |
| #3110 | 139 |