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 |
|---|---|---|
| 2. C2×#17984077 | C2 | semidirect |
| 3. #41×Dic137 | C2 | semidirect |
| 4. #22577627 | C2 | semidirect |
| 5. #22577620 | C2 | semidirect |
| 6. #22577426 | C2 | semidirect |
| 7. #22577412 | C2 | semidirect |
| 8. #22577409 | C2 | semidirect |
| 9. C2×#137×C137 | C2 | semidirect |
| 18. Q8×Dic137 | C22 | semidirect |
| 20. D4×Dic137 | C22 | semidirect |
| 26. #17984017 | C22 | semidirect |
| 27. #17984012 | C22 | semidirect |
| 32. C2×Q16×C137 | C22 | semidirect |
| 33. C2×SD16×C137 | C22 | semidirect |
| 125. C137 | #3040 | semidirect |
| 127. C2×#137 | D137 | semidirect |
| 141. C2×Q16 | C2×D137 | semidirect |
| 143. C2×SD16 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984113 | 2 |
| C2×#17984077 | 2 |
| #41×Dic137 | 2 |
| #22577627 | 2 |
| #22577620 | 2 |
| #22577426 | 2 |
| #22577412 | 2 |
| #22577409 | 2 |
| C2×#137×C137 | 2 |
| #3040 | 137 |