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. #22578449 | C2 | semidirect |
| 2. #22578444 | C2 | semidirect |
| 3. #22578327 | C2 | semidirect |
| 4. #22578321 | C2 | semidirect |
| 5. #22578320 | C2 | semidirect |
| 6. #22578294 | C2 | semidirect |
| 18. #17984031 | C4 | semidirect |
| 19. D2192 | C4 | semidirect |
| 20. #17984029 | C4 | semidirect |
| 22. SD32×C137 | C4 | semidirect |
| 36. D1096 | C2×C4 | semidirect |
| 39. #14555485 | C2×C4 | semidirect |
| 40. Q16×C137 | C2×C4 | semidirect |
| 42. C16×C137 | C2×C4 | semidirect |
| 75. C137 | AGL(1,ℤ/16) | semidirect |
| 89. SD32 | #10587739 | semidirect |
| 102. Q16 | 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 |
|---|---|
| #22578449 | 2 |
| #22578444 | 2 |
| #22578327 | 2 |
| #22578321 | 2 |
| #22578320 | 2 |
| #22578294 | 2 |
| #22577840 | 2 |
| AGL(1,ℤ/16) | 137 |