Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 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. #22582925 | C2 | semidirect |
| 2. #22582905 | C2 | semidirect |
| 3. #22582904 | C2 | semidirect |
| 4. #22582899 | C2 | semidirect |
| 5. C2×#17985123 | C2 | semidirect |
| 6. #22582886 | C2 | semidirect |
| 7. H(5,𝔽2)×C281 | C2 | semidirect |
| 9. #17985138 | C22 | semidirect |
| 10. C2×D1124 | C22 | semidirect |
| 12. #17985128 | C22 | semidirect |
| 13. #17985126 | C22 | semidirect |
| 14. #17985125 | C22 | semidirect |
| 15. #17985123 | C22 | semidirect |
| 16. #17985123 | C22 | semidirect |
| 17. #17985122 | C22 | semidirect |
| 18. C2×#14555886 | C22 | semidirect |
| 21. #41×C281 | C22 | semidirect |
| 23. C2×D4×C281 | C22 | semidirect |
| 54. C281 | #576 | semidirect |
| 57. H(5,𝔽2) | D281 | semidirect |
| 67. #41 | C2×D281 | semidirect |
| 71. C2×D4 | C2×D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582925 | 2 |
| #22582905 | 2 |
| #22582904 | 2 |
| #22582899 | 2 |
| C2×#17985123 | 2 |
| #22582886 | 2 |
| H(5,𝔽2)×C281 | 2 |
| #576 | 281 |