Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 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. #22578482 | C2 | semidirect |
| 2. #41×#10587739 | C2 | semidirect |
| 3. #22578402 | C2 | semidirect |
| 4. #22578400 | C2 | semidirect |
| 5. C2×#17984153 | C2 | semidirect |
| 6. D137⋊#104 | C2 | semidirect |
| 10. C2×#14555520 | C22 | semidirect |
| 11. D137⋊M16 | C22 | semidirect |
| 14. #17984167 | C22 | semidirect |
| 15. C2×C4×#10587739 | C22 | semidirect |
| 16. #17984153 | C22 | semidirect |
| 17. #17984153 | C22 | semidirect |
| 18. #17984153 | C22 | semidirect |
| 19. #17984152 | C22 | semidirect |
| 20. #17984152 | C22 | semidirect |
| 22. #17984136 | C4 | semidirect |
| 24. #17984134 | C4 | semidirect |
| 25. #17984134 | C4 | semidirect |
| 31. 2−1+4×C137 | C4 | semidirect |
| 48. #14555511 | C2×C4 | semidirect |
| 55. #14555510 | C2×C4 | semidirect |
| 60. Q8×D137 | C2×C4 | semidirect |
| 64. C2×D548 | C2×C4 | semidirect |
| 68. D4×D137 | C2×C4 | semidirect |
| 75. #41×C137 | C2×C4 | semidirect |
| 77. C2×Q8×C137 | C2×C4 | semidirect |
| 139. C137 | #2901 | semidirect |
| 150. 2−1+4 | #10587739 | semidirect |
| 189. #41 | C2×#10587739 | semidirect |
| 194. C2×Q8 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578482 | 2 |
| #41×#10587739 | 2 |
| #22578402 | 2 |
| #22578400 | 2 |
| C2×#17984153 | 2 |
| D137⋊#104 | 2 |
| #22578240 | 2 |
| #2901 | 137 |