Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984136 | C2 | semidirect |
| 2. C2×#17984114 | C2 | semidirect |
| 3. #22577970 | C2 | semidirect |
| 4. #22577547 | C2 | semidirect |
| 5. #22577540 | C2 | semidirect |
| 6. #22577412 | C2 | semidirect |
| 7. #22577400 | C2 | semidirect |
| 8. #22577369 | C2 | semidirect |
| 9. C22×SD16×C137 | C2 | semidirect |
| 13. C2×#14555511 | C22 | semidirect |
| 18. C2×Q8×D137 | C22 | semidirect |
| 28. #17984013 | C22 | semidirect |
| 29. #17984012 | C22 | semidirect |
| 30. #17984010 | C22 | semidirect |
| 31. #17984000 | C22 | semidirect |
| 44. #14555510 | D4 | semidirect |
| 72. C2×Q8×C137 | D4 | semidirect |
| 145. C137 | #3010 | semidirect |
| 149. C22×SD16 | D137 | semidirect |
| 200. C2×Q8 | C22⋊D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984136 | 2 |
| C2×#17984114 | 2 |
| #22577970 | 2 |
| #22577547 | 2 |
| #22577540 | 2 |
| #22577412 | 2 |
| #22577400 | 2 |
| #22577369 | 2 |
| C22×SD16×C137 | 2 |
| #3010 | 137 |