Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
356 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 166 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. #22578455 | C2 | semidirect |
| 2. #22578454 | C2 | semidirect |
| 3. Q8×#11764047 | C2 | semidirect |
| 31. #14555520 | Q8 | semidirect |
| 90. C137 | #2962 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578455 | 2 |
| #22578454 | 2 |
| Q8×#11764047 | 2 |
| #22578410 | 2 |
| #22578404 | 2 |
| #22578368 | 2 |
| C4×#14555520 | 2 |
| #22577958 | 2 |
| #2962 | 137 |