Finite Group DatabasebetaFinite Group DatabasebetaOrder 17728.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×#17984563 | C2 | semidirect |
| 2. #22579906 | C2 | direct (N × H) |
| 3. C2×#17984551 | C2 | semidirect |
| 4. C2×#17984548 | C2 | semidirect |
| 5. C2×#17984547 | C2 | semidirect |
| 6. C22×D4×C277 | C2 | semidirect |
| 8. #17984563 | C22 | semidirect |
| 9. C2×Dic554 | C22 | semidirect |
| 10. C2×D1108 | C22 | semidirect |
| 13. #17984551 | C22 | semidirect |
| 14. #17984548 | C22 | semidirect |
| 15. #17984547 | C22 | semidirect |
| 16. C2×#14555660 | C22 | semidirect |
| 21. C2×D4×C277 | C22 | semidirect |
| 25. Dic554 | C23 | semidirect |
| 27. D1108 | C23 | semidirect |
| 31. #14555660 | C23 | semidirect |
| 57. C2×C277 | AGL(1,ℤ/8) | semidirect |
| 60. C277 | C2×AGL(1,ℤ/8) | semidirect |
| 63. C22×D4 | D277 | semidirect |
| 77. C2×D4 | C2×D277 | semidirect |
| 119. C2 | #22579906 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984563 | 2 |
| #22579906 | 2 |
| C2×#17984551 | 2 |
| C2×#17984548 | 2 |
| C2×#17984547 | 2 |
| C22×D4×C277 | 2 |
| C2×AGL(1,ℤ/8) | 277 |