Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
520 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 185 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×#17984096 | C2 | semidirect |
| 2. C22×C8×D137 | C2 | semidirect |
| 4. #22577473 | C2 | semidirect |
| 5. #22577468 | C2 | semidirect |
| 6. #22577369 | C2 | semidirect |
| 7. #22577366 | C2 | semidirect |
| 8. #22577359 | C2 | semidirect |
| 9. #424×C137 | C2 | semidirect |
| 14. C2×#14555493 | C22 | semidirect |
| 19. C2×C8×D137 | C22 | semidirect |
| 26. #17984000 | C22 | semidirect |
| 27. #17983999 | C22 | semidirect |
| 28. C4×#11764040 | C22 | semidirect |
| 32. C4⋊C8×C137 | C22 | semidirect |
| 48. C2×#11764040 | D4 | semidirect |
| 101. C2×D137 | #131 | semidirect |
| 113. C137 | #2929 | semidirect |
| 120. #424 | D137 | semidirect |
| 142. 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×#17984096 | 2 |
| C22×C8×D137 | 2 |
| #22577915 | 2 |
| #22577473 | 2 |
| #22577468 | 2 |
| #22577369 | 2 |
| #22577366 | 2 |
| #22577359 | 2 |
| #424×C137 | 2 |
| #2929 | 137 |