Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
752 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 752 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. C22×#14555773 | C2 | semidirect |
| 3. #22581524 | C2 | semidirect |
| 4. #22581115 | C2 | semidirect |
| 5. #22581104 | C2 | semidirect |
| 6. #22580958 | C2 | semidirect |
| 7. #22580949 | C2 | semidirect |
| 8. #22580920 | C2 | semidirect |
| 10. C22×Dic278 | C22 | semidirect |
| 12. C2×#14555775 | C22 | semidirect |
| 14. C2×#14555773 | C22 | semidirect |
| 15. C2×#14555773 | C22 | semidirect |
| 16. C2×#14555769 | C22 | semidirect |
| 17. C22×C139⋊C8 | C22 | semidirect |
| 21. #17984821 | C22 | semidirect |
| 22. #17984801 | C22 | semidirect |
| 23. #17984766 | C22 | semidirect |
| 24. #17984763 | C22 | semidirect |
| 25. #17984763 | C22 | semidirect |
| 26. C22⋊(C139⋊C8) | C22 | semidirect |
| 146. C139 | #3009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984872 | 2 |
| C22×#14555773 | 2 |
| #22581524 | 2 |
| #22581115 | 2 |
| #22581104 | 2 |
| #22580958 | 2 |
| #22580949 | 2 |
| #22580920 | 2 |
| C2×H(5,𝔽2)×C139 | 2 |
| #3009 | 139 |