Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
472 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 162 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×#17984175 | C2 | semidirect |
| 2. #22578445 | C2 | direct (N × H) |
| 3. C2×#17984159 | C2 | semidirect |
| 4. C2×#17984152 | C2 | semidirect |
| 5. C2×C8×#10587739 | C2 | semidirect |
| 8. #17984175 | C22 | semidirect |
| 14. #17984159 | C22 | semidirect |
| 15. #17984152 | C22 | semidirect |
| 16. C8×#10587739 | C22 | semidirect |
| 18. #17984107 | C4 | semidirect |
| 20. C2×Dic548 | C4 | semidirect |
| 21. C2×#14555498 | C4 | semidirect |
| 23. C2×D8×C137 | C4 | semidirect |
| 44. Dic548 | C2×C4 | semidirect |
| 45. #14555498 | C2×C4 | semidirect |
| 50. D8×C137 | C2×C4 | semidirect |
| 89. C2×C137 | #443 | semidirect |
| 93. C137 | C2×#443 | semidirect |
| 106. C2×D8 | #10587739 | semidirect |
| 130. D8 | C2×#10587739 | semidirect |
| 185. C2 | #22578445 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984175 | 2 |
| #22578445 | 2 |
| C2×#17984159 | 2 |
| C2×#17984152 | 2 |
| C2×C8×#10587739 | 2 |
| C2×#17984107 | 2 |
| C2×#443 | 137 |