Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
458 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. #22578169 | C2 | semidirect |
| 3. #22577526 | C2 | semidirect |
| 4. #22577521 | C2 | semidirect |
| 5. #22577452 | C2 | semidirect |
| 6. C2×#17984016 | C2 | semidirect |
| 7. C4×M16×C137 | C2 | semidirect |
| 9. #17984121 | C4 | semidirect |
| 10. #17984116 | C4 | semidirect |
| 13. #17984094 | C22 | semidirect |
| 16. #17984024 | C22 | semidirect |
| 17. #17984016 | C22 | semidirect |
| 18. #17984016 | C22 | semidirect |
| 22. #97×C137 | C22 | semidirect |
| 23. C4×C8×C137 | C22 | semidirect |
| 32. Dic548 | C2×C4 | semidirect |
| 33. #14555499 | C2×C4 | semidirect |
| 34. D1096 | C2×C4 | semidirect |
| 85. C137 | #2956 | semidirect |
| 93. C4×M16 | D137 | semidirect |
| 108. #97 | C2×D137 | semidirect |
| 109. C4×C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578203 | 2 |
| #22578169 | 2 |
| #22577526 | 2 |
| #22577521 | 2 |
| #22577452 | 2 |
| C2×#17984016 | 2 |
| C4×M16×C137 | 2 |
| #2956 | 137 |