Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 2. C2×#17984096 | C2 | semidirect |
| 3. #22577524 | C2 | semidirect |
| 4. #22577519 | C2 | semidirect |
| 5. #22577419 | C2 | semidirect |
| 6. #22577361 | C2 | semidirect |
| 7. #430×C137 | C2 | semidirect |
| 9. #17984121 | C4 | semidirect |
| 10. #17984116 | C4 | semidirect |
| 14. #17984096 | C22 | semidirect |
| 15. #17984096 | C22 | semidirect |
| 20. #17984014 | C22 | semidirect |
| 21. #17983998 | C22 | semidirect |
| 22. C8×Dic137 | C22 | semidirect |
| 25. #108×C137 | C22 | semidirect |
| 89. C137 | #2955 | semidirect |
| 95. #430 | D137 | semidirect |
| 112. #108 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578203 | 2 |
| C2×#17984096 | 2 |
| #22577524 | 2 |
| #22577519 | 2 |
| #22577419 | 2 |
| #22577361 | 2 |
| #430×C137 | 2 |
| #2955 | 137 |