Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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. C4⋊Q8×D137 | C2 | semidirect |
| 3. #22577765 | C2 | semidirect |
| 4. #22577763 | C2 | semidirect |
| 5. #22577762 | C2 | semidirect |
| 6. #22577752 | C2 | semidirect |
| 7. #22577748 | C2 | semidirect |
| 8. #22577403 | C2 | semidirect |
| 9. #22577401 | C2 | semidirect |
| 10. #22577355 | C2 | semidirect |
| 11. #489×C137 | C2 | semidirect |
| 140. C137 | #3141 | semidirect |
| 147. #489 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577952 | 2 |
| C4⋊Q8×D137 | 2 |
| #22577765 | 2 |
| #22577763 | 2 |
| #22577762 | 2 |
| #22577752 | 2 |
| #22577748 | 2 |
| #22577403 | 2 |
| #22577401 | 2 |
| #22577355 | 2 |
| #489×C137 | 2 |
| #3141 | 137 |