Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984868 | C2 | semidirect |
| 3. #22581120 | C2 | direct (N × H) |
| 4. C2×#17984770 | C2 | semidirect |
| 5. C2×#17984759 | C2 | semidirect |
| 6. C2×#127×C139 | C2 | semidirect |
| 9. #17984887 | C22 | semidirect |
| 15. #17984868 | C22 | semidirect |
| 18. C2×#14555769 | C22 | semidirect |
| 19. #17984770 | C22 | semidirect |
| 20. #17984759 | C22 | semidirect |
| 23. C22×D4×C139 | C22 | semidirect |
| 25. #127×C139 | C22 | semidirect |
| 26. C2×C42×C139 | C22 | semidirect |
| 30. #14555785 | D4 | semidirect |
| 34. C2×Dic278 | D4 | semidirect |
| 35. C2×D556 | D4 | semidirect |
| 47. #14555769 | C23 | semidirect |
| 60. C2×D4×C139 | C23 | semidirect |
| 64. C42×C139 | C23 | semidirect |
| 69. Dic278 | C2×D4 | semidirect |
| 71. D556 | C2×D4 | semidirect |
| 123. C2×C139 | #453 | semidirect |
| 126. C139 | C2×#453 | semidirect |
| 130. C2×#127 | D139 | semidirect |
| 143. C22×D4 | C2×D139 | semidirect |
| 150. #127 | C2×D139 | semidirect |
| 151. C2×C42 | C2×D139 | semidirect |
| 180. C2×D4 | C22×D139 | semidirect |
| 191. C42 | C22×D139 | semidirect |
| 251. C2 | #22581120 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984887 | 2 |
| C2×#17984868 | 2 |
| #22581120 | 2 |
| C2×#17984770 | 2 |
| C2×#17984759 | 2 |
| C2×#127×C139 | 2 |
| C2×#453 | 139 |