Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22578493 | C2 | semidirect |
| 3. #22578492 | C2 | semidirect |
| 27. C2×#11764040 | C8 | semidirect |
| 28. C8×D137 | C8 | semidirect |
| 29. C8×D137 | C8 | semidirect |
| 32. C2×C8×C137 | C8 | semidirect |
| 71. C137 | #1564 | semidirect |
| 100. C2×C8 | #11764049 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578516 | 2 |
| #22578493 | 2 |
| #22578492 | 2 |
| C2×C8×#10587739 | 2 |
| #1564 | 137 |