Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
292 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 90 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 |
|---|---|---|
| 3. #22578368 | C2 | semidirect |
| 4. C2×#17984142 | C2 | semidirect |
| 5. #22578279 | C2 | semidirect |
| 6. #22578273 | C2 | semidirect |
| 9. #17984176 | C4 | semidirect |
| 16. #17984153 | C4 | semidirect |
| 23. #17984012 | C4 | semidirect |
| 24. #17984010 | C4 | semidirect |
| 25. #17984008 | C4 | semidirect |
| 26. #103×C137 | C4 | semidirect |
| 109. C137 | #1765 | semidirect |
| 131. #103 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984176 | 2 |
| C2×#17984153 | 2 |
| #22578368 | 2 |
| C2×#17984142 | 2 |
| #22578279 | 2 |
| #22578273 | 2 |
| #22577398 | 2 |
| #1765 | 137 |