Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22581789 | C2 | semidirect |
| 2. C2×#17984870 | C2 | semidirect |
| 3. #22581517 | C2 | semidirect |
| 4. #22581128 | C2 | semidirect |
| 5. #22581123 | C2 | semidirect |
| 6. #22580969 | C2 | semidirect |
| 7. #413×C139 | C2 | semidirect |
| 8. #17984890 | C22 | semidirect |
| 12. #17984887 | C22 | semidirect |
| 16. C22×D556 | C22 | semidirect |
| 18. #17984870 | C22 | semidirect |
| 21. #17984838 | C22 | semidirect |
| 22. #17984831 | C22 | semidirect |
| 25. #17984801 | C22 | semidirect |
| 26. #17984768 | C22 | semidirect |
| 28. C2×M16×C139 | C22 | semidirect |
| 29. #101×C139 | C22 | semidirect |
| 30. #100×C139 | C22 | semidirect |
| 38. #14555785 | D4 | semidirect |
| 43. C2×Dic278 | D4 | semidirect |
| 49. C2×D556 | D4 | semidirect |
| 134. C139 | #3021 | semidirect |
| 142. #413 | D139 | semidirect |
| 157. C2×M16 | C2×D139 | semidirect |
| 164. #101 | C2×D139 | semidirect |
| 165. #100 | C2×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581789 | 2 |
| C2×#17984870 | 2 |
| #22581517 | 2 |
| #22581128 | 2 |
| #22581123 | 2 |
| #22580969 | 2 |
| #413×C139 | 2 |
| #3021 | 139 |