Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
374 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 68 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. #22578350 | C2 | semidirect |
| 4. #22578280 | C2 | semidirect |
| 19. #17984003 | C4 | semidirect |
| 20. #17984002 | C4 | semidirect |
| 21. #99×C137 | C4 | semidirect |
| 48. C22⋊Dic137 | C2×C4 | semidirect |
| 51. C22⋊C4×C137 | C2×C4 | semidirect |
| 72. C22×D137 | C4⋊C4 | semidirect |
| 81. C2×Dic137 | C4⋊C4 | semidirect |
| 86. C23×C137 | C4⋊C4 | semidirect |
| 90. C2×C4×C137 | C4⋊C4 | semidirect |
| 127. C137 | #1867 | semidirect |
| 147. #99 | #10587739 | semidirect |
| 178. C22⋊C4 | C2×#10587739 | semidirect |
| 191. C23 | C4⋊#10587739 | semidirect |
| 218. C2×C4 | C4⋊#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578470 | 2 |
| #22578351 | 2 |
| #22578350 | 2 |
| #22578280 | 2 |
| #99×D137 | 2 |
| #1867 | 137 |