Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#17984121 | C2 | semidirect |
| 3. C22×Dic548 | C2 | semidirect |
| 4. #22577974 | C2 | semidirect |
| 5. #22577567 | C2 | semidirect |
| 6. #22577561 | C2 | semidirect |
| 7. #22577413 | C2 | semidirect |
| 8. #22577400 | C2 | semidirect |
| 9. #408×C137 | C2 | semidirect |
| 140. C137 | #3011 | semidirect |
| 150. #408 | D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984135 | 2 |
| C2×#17984121 | 2 |
| C22×Dic548 | 2 |
| #22577974 | 2 |
| #22577567 | 2 |
| #22577561 | 2 |
| #22577413 | 2 |
| #22577400 | 2 |
| #408×C137 | 2 |
| #3011 | 137 |