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. #22578309 | C2 | semidirect |
| 3. #22578307 | C2 | semidirect |
| 9. #17984084 | C4 | semidirect |
| 11. #17984077 | C4 | semidirect |
| 15. #17984047 | C4 | semidirect |
| 16. C2×#41×C137 | C4 | semidirect |
| 31. C4×Dic137 | C2×C4 | semidirect |
| 32. C4×Dic137 | C2×C4 | semidirect |
| 34. C2×Q8×C137 | C2×C4 | semidirect |
| 36. C2×D4×C137 | C2×C4 | semidirect |
| 86. C137 | #2127 | semidirect |
| 92. C2×#41 | #10587739 | semidirect |
| 106. C2×Q8 | C2×#10587739 | semidirect |
| 114. C2×D4 | 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 |
| #22578309 | 2 |
| #22578307 | 2 |
| #22577967 | 2 |
| #2127 | 137 |