Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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×#17984872 | C2 | semidirect |
| 2. C2×#17984829 | C2 | semidirect |
| 3. #22581131 | C2 | direct (N × H) |
| 4. C2×#17984769 | C2 | semidirect |
| 5. C2×#17984759 | C2 | semidirect |
| 7. C22×Dic278 | C22 | semidirect |
| 9. #17984872 | C22 | semidirect |
| 12. C2×#14555769 | C22 | semidirect |
| 14. #17984829 | C22 | semidirect |
| 16. C2×C4×Dic139 | C22 | semidirect |
| 17. #17984769 | C22 | semidirect |
| 18. #17984759 | C22 | semidirect |
| 30. C2×Dic278 | C23 | semidirect |
| 36. #14555769 | C23 | semidirect |
| 40. C4×Dic139 | C23 | semidirect |
| 117. C2×C139 | #455 | semidirect |
| 119. C139 | C2×#455 | semidirect |
| 237. C2 | #22581131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984872 | 2 |
| C2×#17984829 | 2 |
| #22581131 | 2 |
| C2×#17984769 | 2 |
| C2×#17984759 | 2 |
| C2×H(5,𝔽2)×C139 | 2 |
| C2×#455 | 139 |