Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
488 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 488 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. #22581503 | C2 | semidirect |
| 2. C2×C4×D556 | C2 | semidirect |
| 3. #22581272 | C2 | semidirect |
| 4. #22581244 | C2 | semidirect |
| 5. #22581149 | C2 | semidirect |
| 6. #22581089 | C2 | semidirect |
| 7. #22581066 | C2 | semidirect |
| 8. #432×C139 | C2 | semidirect |
| 13. #17984842 | C22 | semidirect |
| 14. #17984839 | C22 | semidirect |
| 23. C4×D556 | C22 | semidirect |
| 26. #17984774 | C22 | semidirect |
| 28. #17984764 | C22 | semidirect |
| 30. C4⋊C8×C139 | C22 | semidirect |
| 32. #97×C139 | C22 | semidirect |
| 76. D556 | #41 | semidirect |
| 120. C139 | #3109 | semidirect |
| 129. #432 | D139 | semidirect |
| 149. C4⋊C8 | C2×D139 | semidirect |
| 153. #97 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581503 | 2 |
| C2×C4×D556 | 2 |
| #22581272 | 2 |
| #22581244 | 2 |
| #22581149 | 2 |
| #22581089 | 2 |
| #22581066 | 2 |
| #432×C139 | 2 |
| #3109 | 139 |