Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
738 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 249 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. #22578170 | C2 | semidirect |
| 3. #22577421 | C2 | semidirect |
| 4. C2×#17984016 | C2 | semidirect |
| 5. C4×#41×C137 | C2 | semidirect |
| 7. #17984135 | C4 | semidirect |
| 8. #17984134 | C4 | semidirect |
| 13. C2×#14555494 | C22 | semidirect |
| 14. #17984016 | C22 | semidirect |
| 15. #17984016 | C22 | semidirect |
| 19. #117×C137 | C22 | semidirect |
| 20. C2×C42×C137 | C22 | semidirect |
| 24. #14555510 | C2×C4 | semidirect |
| 27. C2×Dic274 | C2×C4 | semidirect |
| 29. C2×D548 | C2×C4 | semidirect |
| 83. C137 | #2901 | semidirect |
| 87. C4×#41 | D137 | semidirect |
| 101. #117 | C2×D137 | semidirect |
| 102. C2×C42 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578239 | 2 |
| #22578170 | 2 |
| #22577421 | 2 |
| C2×#17984016 | 2 |
| C4×#41×C137 | 2 |
| #2901 | 137 |