Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
380 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 80 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. #22578345 | C2 | semidirect |
| 3. #22578281 | C2 | semidirect |
| 10. C22×C4×D137 | C4 | semidirect |
| 14. C2×C4⋊Dic137 | C4 | semidirect |
| 15. C2×#14555487 | C4 | semidirect |
| 17. C2×C42×C137 | C4 | semidirect |
| 53. C22×D137 | C4⋊C4 | semidirect |
| 76. C2×C4×C137 | C4⋊C4 | semidirect |
| 98. C4×C137 | #99 | semidirect |
| 109. C137 | #1799 | semidirect |
| 125. C2×C42 | #10587739 | semidirect |
| 186. C2×C4 | C4⋊#10587739 | semidirect |
| 210. C4 | #17984147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984147 | 2 |
| #22578345 | 2 |
| #22578281 | 2 |
| C2×C4×D548 | 2 |
| #1799 | 137 |