Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #22577501 | C2 | semidirect |
| 4. C4×#14555497 | C2 | semidirect |
| 5. #22577439 | C2 | semidirect |
| 6. #22577412 | C2 | semidirect |
| 8. #22577359 | C2 | semidirect |
| 9. #519×C137 | C2 | semidirect |
| 11. C2×#14555497 | C4 | semidirect |
| 20. #17984021 | C22 | semidirect |
| 21. #17984019 | C22 | semidirect |
| 22. #17984012 | C22 | semidirect |
| 24. #17983999 | C22 | semidirect |
| 25. C4×#11764040 | C22 | semidirect |
| 28. C4×Q8×C137 | C22 | semidirect |
| 38. #14555497 | C2×C4 | semidirect |
| 39. #14555497 | C2×C4 | semidirect |
| 41. C2×#11764040 | C2×C4 | semidirect |
| 51. C2×Q8×C137 | C2×C4 | semidirect |
| 103. C137 | #2949 | semidirect |
| 106. #519 | D137 | semidirect |
| 122. C4×Q8 | C2×D137 | semidirect |
| 139. C2×Q8 | C4×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555497 | 2 |
| #22577877 | 2 |
| #22577501 | 2 |
| C4×#14555497 | 2 |
| #22577439 | 2 |
| #22577412 | 2 |
| #22577407 | 2 |
| #22577359 | 2 |
| #519×C137 | 2 |
| #2949 | 137 |