Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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. #22578015 | C2 | semidirect |
| 3. #22577745 | C2 | semidirect |
| 4. #22577704 | C2 | semidirect |
| 5. #22577609 | C2 | semidirect |
| 7. #22577505 | C2 | semidirect |
| 8. C4×#14555499 | C2 | semidirect |
| 9. #433×C137 | C2 | semidirect |
| 13. #17984088 | C22 | semidirect |
| 15. #17984080 | C22 | semidirect |
| 18. C4×Dic274 | C22 | semidirect |
| 24. #17984022 | C22 | semidirect |
| 25. #17984020 | C22 | semidirect |
| 26. #17984013 | C22 | semidirect |
| 27. #17984013 | C22 | semidirect |
| 31. C4⋊C8×C137 | C22 | semidirect |
| 33. #97×C137 | C22 | semidirect |
| 34. C4×C8×C137 | C22 | semidirect |
| 102. C137 | #3123 | semidirect |
| 112. #433 | D137 | semidirect |
| 130. C4⋊C8 | C2×D137 | semidirect |
| 136. #97 | C2×D137 | semidirect |
| 137. C4×C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578015 | 2 |
| #22577877 | 2 |
| #22577745 | 2 |
| #22577704 | 2 |
| #22577609 | 2 |
| #22577556 | 2 |
| #22577505 | 2 |
| C4×#14555499 | 2 |
| #433×C137 | 2 |
| #3123 | 137 |