Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
462 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22581663 | C2 | semidirect |
| 3. #22581300 | C2 | semidirect |
| 4. #22581273 | C2 | semidirect |
| 5. #22581243 | C2 | semidirect |
| 6. #22581185 | C2 | semidirect |
| 7. #22581153 | C2 | semidirect |
| 8. #22581102 | C2 | semidirect |
| 9. C8×D556 | C2 | semidirect |
| 10. #102×D139 | C2 | semidirect |
| 11. C4×SD16×C139 | C2 | semidirect |
| 14. C2×#14555772 | C22 | semidirect |
| 15. C2×C8×D139 | C22 | semidirect |
| 16. #17984842 | C22 | semidirect |
| 20. #17984818 | C22 | semidirect |
| 26. C4⋊C4×D139 | C22 | semidirect |
| 27. #17984773 | C22 | semidirect |
| 28. C4⋊(C139⋊C8) | C22 | semidirect |
| 29. #17984764 | C22 | semidirect |
| 30. #17984764 | C22 | semidirect |
| 32. #17984762 | C22 | semidirect |
| 33. (C2×D139)⋊C8 | C22 | semidirect |
| 35. C4×Q8×C139 | C22 | semidirect |
| 37. #106×C139 | C22 | semidirect |
| 38. #103×C139 | C22 | semidirect |
| 40. C4×C8×C139 | C22 | semidirect |
| 88. D556 | SD16 | semidirect |
| 136. C139 | #3295 | semidirect |
| 146. C4×SD16 | D139 | semidirect |
| 162. C4×Q8 | C2×D139 | semidirect |
| 168. #106 | C2×D139 | semidirect |
| 170. #103 | C2×D139 | semidirect |
| 177. C4×C8 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581663 | 2 |
| D4×D556 | 2 |
| #22581300 | 2 |
| #22581273 | 2 |
| #22581243 | 2 |
| #22581185 | 2 |
| #22581153 | 2 |
| #22581102 | 2 |
| C8×D556 | 2 |
| #102×D139 | 2 |
| C4×SD16×C139 | 2 |
| #3295 | 139 |