Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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×#17984095 | C2 | semidirect |
| 2. #22577525 | C2 | semidirect |
| 3. #22577520 | C2 | semidirect |
| 4. #22577452 | C2 | semidirect |
| 5. #22577420 | C2 | semidirect |
| 6. #22577361 | C2 | semidirect |
| 10. #17984095 | C22 | semidirect |
| 11. #17984095 | C22 | semidirect |
| 17. #17984024 | C22 | semidirect |
| 18. #17984015 | C22 | semidirect |
| 19. #17983998 | C22 | semidirect |
| 20. C8×Dic137 | C22 | semidirect |
| 22. #137×C137 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C137 | C4 | semidirect |
| 89. C137 | #2955 | semidirect |
| 99. #137 | Dic137 | semidirect |
| 100. AGL(1,ℤ/8) | Dic137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984095 | 2 |
| #22577525 | 2 |
| #22577520 | 2 |
| #22577452 | 2 |
| #22577420 | 2 |
| #22577361 | 2 |
| #575×C137 | 2 |
| #2955 | 137 |