Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
480 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 3. C2×#17984086 | C2 | semidirect |
| 5. #22577612 | C2 | semidirect |
| 6. #22577607 | C2 | semidirect |
| 7. #22577426 | C2 | semidirect |
| 8. #22577411 | C2 | semidirect |
| 9. #419×C137 | C2 | semidirect |
| 116. Dic137 | #137 | semidirect |
| 121. C137 | #3039 | semidirect |
| 131. #419 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984121 | 2 |
| C2×#17984119 | 2 |
| C2×#17984086 | 2 |
| #22577871 | 2 |
| #22577612 | 2 |
| #22577607 | 2 |
| #22577426 | 2 |
| #22577411 | 2 |
| #419×C137 | 2 |
| #3039 | 137 |