Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 2. C2×#17984094 | C2 | semidirect |
| 3. #22577526 | C2 | semidirect |
| 4. #22577521 | C2 | semidirect |
| 5. #22577452 | C2 | semidirect |
| 6. #22577421 | C2 | semidirect |
| 7. #405×C137 | C2 | semidirect |
| 9. #17984121 | C4 | semidirect |
| 10. #17984116 | C4 | semidirect |
| 14. #17984094 | C22 | semidirect |
| 15. #17984094 | C22 | semidirect |
| 19. #17984024 | C22 | semidirect |
| 20. #17984016 | C22 | semidirect |
| 24. #97×C137 | C22 | semidirect |
| 25. C4×C8×C137 | C22 | semidirect |
| 89. C137 | #2955 | semidirect |
| 97. #405 | D137 | semidirect |
| 114. #97 | C2×D137 | semidirect |
| 115. C4×C8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578203 | 2 |
| C2×#17984094 | 2 |
| #22577526 | 2 |
| #22577521 | 2 |
| #22577452 | 2 |
| #22577421 | 2 |
| #405×C137 | 2 |
| #2955 | 137 |