Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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. C2×#17984119 | C2 | semidirect |
| 3. C4×#14555510 | C2 | semidirect |
| 4. #22577622 | C2 | semidirect |
| 5. #22577615 | C2 | semidirect |
| 6. #22577427 | C2 | semidirect |
| 7. #22577412 | C2 | semidirect |
| 8. #22577408 | C2 | semidirect |
| 9. C2×#124×C137 | C2 | semidirect |
| 13. C2×#14555500 | C22 | semidirect |
| 15. C2×#14555497 | C22 | semidirect |
| 19. C4×Dic274 | C22 | semidirect |
| 20. C4×D548 | C22 | semidirect |
| 25. C4⋊#11764040 | C22 | semidirect |
| 26. #17984012 | C22 | semidirect |
| 125. C137 | #3040 | semidirect |
| 129. C2×#124 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984119 | 2 |
| C2×#17984114 | 2 |
| C4×#14555510 | 2 |
| #22577622 | 2 |
| #22577615 | 2 |
| #22577427 | 2 |
| #22577412 | 2 |
| #22577408 | 2 |
| C2×#124×C137 | 2 |
| #3040 | 137 |