Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
334 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 62 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. #22578375 | C2 | semidirect |
| 2. C2×(C2×#10587739)⋊C4 | C2 | semidirect |
| 3. #22578257 | C2 | semidirect |
| 4. #22578254 | C2 | semidirect |
| 14. #17984064 | C4 | semidirect |
| 16. #17984059 | C4 | semidirect |
| 21. #17984047 | C4 | semidirect |
| 22. C2×#41×C137 | C4 | semidirect |
| 38. C4⋊Dic137 | C2×C4 | semidirect |
| 39. C4⋊Dic137 | C2×C4 | semidirect |
| 49. C2×Q8×C137 | C2×C4 | semidirect |
| 51. C2×D4×C137 | C2×C4 | semidirect |
| 119. C137 | #1504 | semidirect |
| 126. C2×#41 | #10587739 | semidirect |
| 145. C2×Q8 | C2×#10587739 | semidirect |
| 149. C2×D4 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578375 | 2 |
| C2×(C2×#10587739)⋊C4 | 2 |
| #22578257 | 2 |
| #22578254 | 2 |
| #22577910 | 2 |
| #1504 | 137 |