Finite Group DatabasebetaFinite Group DatabasebetaOrder 17984.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 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. #22582926 | C2 | semidirect |
| 2. #22582925 | C2 | semidirect |
| 3. #22582912 | C2 | semidirect |
| 4. #22582907 | C2 | semidirect |
| 5. #22582901 | C2 | semidirect |
| 6. C2×#17985127 | C2 | semidirect |
| 7. #131×C281 | C2 | semidirect |
| 10. #17985138 | C22 | semidirect |
| 12. C2×Dic562 | C22 | semidirect |
| 16. Dic1124 | C22 | semidirect |
| 17. #17985127 | C22 | semidirect |
| 18. #17985127 | C22 | semidirect |
| 19. #17985127 | C22 | semidirect |
| 20. D2248 | C22 | semidirect |
| 22. M16×C281 | C22 | semidirect |
| 23. C2×C8×C281 | C22 | semidirect |
| 53. C281 | #577 | semidirect |
| 61. #131 | D281 | semidirect |
| 76. M16 | C2×D281 | semidirect |
| 77. C2×C8 | C2×D281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22582926 | 2 |
| #22582925 | 2 |
| #22582912 | 2 |
| #22582907 | 2 |
| #22582901 | 2 |
| C2×#17985127 | 2 |
| #131×C281 | 2 |
| #577 | 281 |