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×#17984121 | C2 | semidirect |
| 3. C2×#17984076 | C2 | semidirect |
| 4. C4×#14555510 | C2 | semidirect |
| 5. #22577626 | C2 | semidirect |
| 6. #22577619 | C2 | semidirect |
| 7. #22577413 | C2 | semidirect |
| 8. #22577409 | C2 | semidirect |
| 9. #423×C137 | C2 | semidirect |
| 15. C2×Dic548 | C22 | semidirect |
| 17. C2×#14555499 | C22 | semidirect |
| 22. C4×Dic274 | C22 | semidirect |
| 23. C4×D548 | C22 | semidirect |
| 29. #17984013 | C22 | semidirect |
| 34. C4⋊C8×C137 | C22 | semidirect |
| 125. C137 | #3040 | semidirect |
| 133. #423 | D137 | semidirect |
| 158. C4⋊C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984121 | 2 |
| C2×#17984116 | 2 |
| C2×#17984076 | 2 |
| C4×#14555510 | 2 |
| #22577626 | 2 |
| #22577619 | 2 |
| #22577413 | 2 |
| #22577409 | 2 |
| #423×C137 | 2 |
| #3040 | 137 |