Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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×#17984147 | C2 | semidirect |
| 2. #22578310 | C2 | semidirect |
| 3. #22578308 | C2 | semidirect |
| 8. C2×#14555510 | C4 | semidirect |
| 10. #17984085 | C4 | semidirect |
| 12. #17984076 | C4 | semidirect |
| 16. #117×C137 | C4 | semidirect |
| 22. C2×Dic274 | C2×C4 | semidirect |
| 27. C2×D548 | C2×C4 | semidirect |
| 37. C42×C137 | C2×C4 | semidirect |
| 38. C42×C137 | C2×C4 | semidirect |
| 86. C137 | #2127 | semidirect |
| 100. #117 | #10587739 | semidirect |
| 124. C42 | C2×#10587739 | semidirect |
| 125. C42 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984147 | 2 |
| #22578310 | 2 |
| #22578308 | 2 |
| #22577972 | 2 |
| #2127 | 137 |