Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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. #22577741 | C2 | semidirect |
| 3. #22577736 | C2 | semidirect |
| 4. #22577731 | C2 | semidirect |
| 5. #22577443 | C2 | semidirect |
| 6. #22577412 | C2 | semidirect |
| 18. #17984021 | C22 | semidirect |
| 19. #17984019 | C22 | semidirect |
| 20. #17984012 | C22 | semidirect |
| 21. #17984012 | C22 | semidirect |
| 116. C137 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984047 | 2 |
| #22577741 | 2 |
| #22577736 | 2 |
| #22577731 | 2 |
| #22577443 | 2 |
| #22577412 | 2 |
| #22577367 | 2 |
| C2×C22⋊Q8×C137 | 2 |
| #3095 | 137 |