Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#14555499 | C2 | semidirect |
| 3. #22577979 | C2 | semidirect |
| 4. #22577877 | C2 | semidirect |
| 5. #22577619 | C2 | semidirect |
| 6. #22577609 | C2 | semidirect |
| 7. #22577413 | C2 | semidirect |
| 8. #22577400 | C2 | semidirect |
| 9. #424×C137 | C2 | semidirect |
| 18. #17984088 | C22 | semidirect |
| 19. #17984076 | C22 | semidirect |
| 26. #17984013 | C22 | semidirect |
| 27. #17984013 | C22 | semidirect |
| 28. #17984010 | C22 | semidirect |
| 32. C4⋊C8×C137 | C22 | semidirect |
| 116. C137 | #3042 | semidirect |
| 124. #424 | D137 | semidirect |
| 146. C4⋊C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984116 | 2 |
| C22×#14555499 | 2 |
| #22577979 | 2 |
| #22577877 | 2 |
| #22577619 | 2 |
| #22577609 | 2 |
| #22577413 | 2 |
| #22577400 | 2 |
| #424×C137 | 2 |
| #3042 | 137 |