Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 762 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. C2×#17984887 | C2 | semidirect |
| 2. #22581753 | C2 | semidirect |
| 3. #22581520 | C2 | semidirect |
| 4. #22581133 | C2 | semidirect |
| 5. #22581123 | C2 | semidirect |
| 6. #22580969 | C2 | semidirect |
| 7. C2×#100×C139 | C2 | semidirect |
| 12. C2×#14555785 | C22 | semidirect |
| 17. #17984875 | C22 | semidirect |
| 19. #17984870 | C22 | semidirect |
| 21. #17984838 | C22 | semidirect |
| 22. #17984829 | C22 | semidirect |
| 25. #17984801 | C22 | semidirect |
| 26. #17984768 | C22 | semidirect |
| 28. C2×M16×C139 | C22 | semidirect |
| 29. #100×C139 | C22 | semidirect |
| 35. #14555785 | D4 | semidirect |
| 39. C2×Dic278 | D4 | semidirect |
| 40. C2×Dic278 | C23 | semidirect |
| 41. C2×D556 | D4 | semidirect |
| 42. C2×D556 | C23 | semidirect |
| 61. C4×Dic139 | C23 | semidirect |
| 69. M16×C139 | C23 | semidirect |
| 131. C139 | #3019 | semidirect |
| 139. C2×#100 | D139 | semidirect |
| 154. C2×M16 | C2×D139 | semidirect |
| 161. #100 | C2×D139 | semidirect |
| 197. M16 | C22×D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984887 | 2 |
| #22581753 | 2 |
| #22581520 | 2 |
| #22581133 | 2 |
| #22581123 | 2 |
| #22580969 | 2 |
| C2×#100×C139 | 2 |
| #3019 | 139 |