Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
452 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 158 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. #22578483 | C2 | semidirect |
| 2. #22578449 | C2 | semidirect |
| 3. #22578447 | C2 | semidirect |
| 4. D137⋊#108 | C2 | semidirect |
| 5. #22578402 | C2 | semidirect |
| 6. #22578366 | C2 | semidirect |
| 9. #17984176 | C22 | semidirect |
| 14. #17984159 | C22 | semidirect |
| 15. #17984158 | C22 | semidirect |
| 16. #17984153 | C22 | semidirect |
| 17. #17984142 | C22 | semidirect |
| 18. C8×#10587739 | C22 | semidirect |
| 20. #17984111 | C4 | semidirect |
| 21. #17984111 | C4 | semidirect |
| 24. C2×#14555497 | C4 | semidirect |
| 25. C2×D1096 | C4 | semidirect |
| 27. C2×Q16×C137 | C4 | semidirect |
| 101. C137 | #2957 | semidirect |
| 115. C2×Q16 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578483 | 2 |
| #22578449 | 2 |
| #22578447 | 2 |
| D137⋊#108 | 2 |
| #22578402 | 2 |
| #22578366 | 2 |
| C2×#17984111 | 2 |
| #2957 | 137 |