Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
456 conjugacy classes of subgroups; only the 160 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 160 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. #22578443 | C2 | semidirect |
| 3. Q16×#10587739 | C2 | semidirect |
| 20. C2×Dic548 | C4 | semidirect |
| 21. C2×#14555500 | C4 | semidirect |
| 22. Q16×D137 | C4 | semidirect |
| 23. Q16×D137 | C4 | semidirect |
| 27. C2×Q16×C137 | C4 | semidirect |
| 100. C137 | #2950 | semidirect |
| 116. C2×Q16 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578471 | 2 |
| #22578443 | 2 |
| Q16×#10587739 | 2 |
| #22578413 | 2 |
| #22578396 | 2 |
| #22578366 | 2 |
| C2×Q16×D137 | 2 |
| #2950 | 137 |