Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
154 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 44 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. #22578450 | C2 | semidirect |
| 2. #22578444 | C2 | semidirect |
| 3. #22578328 | C2 | semidirect |
| 4. #22578321 | C2 | semidirect |
| 5. #22578319 | C2 | semidirect |
| 6. #22578294 | C2 | semidirect |
| 18. #17984033 | C4 | semidirect |
| 19. #17984032 | C4 | semidirect |
| 20. #17984029 | C4 | semidirect |
| 22. D16×C137 | C4 | semidirect |
| 34. Dic548 | C2×C4 | semidirect |
| 39. #14555485 | C2×C4 | semidirect |
| 41. D8×C137 | C2×C4 | semidirect |
| 42. C16×C137 | C2×C4 | semidirect |
| 75. C137 | AGL(1,ℤ/16) | semidirect |
| 91. D16 | #10587739 | semidirect |
| 107. D8 | C2×#10587739 | semidirect |
| 118. C16 | C2×#10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578450 | 2 |
| #22578444 | 2 |
| #22578328 | 2 |
| #22578321 | 2 |
| #22578319 | 2 |
| #22578294 | 2 |
| #22577837 | 2 |
| AGL(1,ℤ/16) | 137 |